If f (x) = 1/9 x-2, what is f-1(x)?

Answers

Answer 1

Given:

The function is:

[tex]f(x)=\dfrac{1}{9}x-2[/tex]

To find:

The value of [tex]f^{-1}(x)[/tex].

Solution:

We have,

[tex]f(x)=\dfrac{1}{9}x-2[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=\dfrac{1}{9}x-2[/tex]

Step 2: Interchange x and y.

[tex]x=\dfrac{1}{9}y-2[/tex]

Step 3: Isolate the variable [tex]y[/tex].

[tex]x+2=\dfrac{1}{9}y[/tex]

[tex]9(x+2)=y[/tex]

[tex]9x+18=y[/tex]

[tex]y=9x+18[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=9x+18[/tex]

Therefore, the required function is [tex]f^{-1}(x)=9x+18[/tex].


Related Questions

A ball was kicked off a picnic table at the park and its height, h, in metres, above the ground after time, t, in seconds, is represented by h = 0.5 + 16t- 2t^2.

a) What is the height of the picnic table?

b) Complete the square to determine the maximum height of the ball? ​

Answers

Step-by-step explanation:

the picnic table height is 0.5 because it's the constant

and the maximum height is 28

my answer is in the image above

pls help its my last day of school and a have only a few mins to submit

Answers

Answer:

slope = 1/2

y intercept = 2

slope intercept form = y = 1/2x + 2

Step-by-step explanation:

Answer:

Slope: 2

y-intercept: 2

Slope intercept form: y=2x+2

Step-by-step explanation:

Hope this helps!

Answer the questions.

Answers

Answer:

5.

Objective C

[tex]125x + 200 \geqslant 1200 \\ 125x \geqslant 1000 \\ x \geqslant 8[/tex]

7

[tex]x \: \alpha \: y \\ y = kx \\ 2.00 = k \times 8 \\ k = \frac{2.00}{8} \\ k = 0.25[/tex]

Please help asap!! I will mark you as brainliest :)

Answers

Answer:

3, 0, -5, -6

Step-by-step explanation:

7)

when x= -8, f(x) = 8-5 or 3

when x= -5 f(x) = 5-5 or 0

when x= 0, f(x) = 0-5 or -5

when x=1, f(x) = -1-5 or -6

Which point would not be a solution to the system of linear inequalities shown below? y\ge x+5\hspace{50px}y\ge\frac{2}{3} x+6 y≥x+5y≥ 3 2 ​ x+6 (12, 7) (-12, 1) (-12, 9) (-12, 6)

Answers

Answer:

(12,7) is not a solution

Step-by-step explanation:

Given

[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]

Required

Point that is not a solution

We have:

[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]

Substitute [tex]\frac{2}{3}x + 6[/tex] for y in the first inequality

[tex]\frac{2}{3}x + 6 \ge x + 5[/tex]

Collect like terms

[tex]\frac{2}{3}x - x \ge 5-6[/tex]

[tex]-\frac{1}{3}x \ge -1[/tex]

Solve for x (the inequality will change because we are to divide by a  negative number_

[tex]x \le -1/-\frac{1}{3}[/tex]

[tex]x \le 3[/tex]

Without solving further, we can conclude that the first option is not a solution.

Because (12,7) implies that [tex]x =12[/tex]

Compare [tex]x =12[/tex] to [tex]x \le 3[/tex], then [tex]x \le 3[/tex] is false

A regular hexagon has a perimeter of 150 m. Find its area. Leave your answer in the simplest radical form.

Answers

Answer:

1623.80 m²

√3(1875/2) m²

Step-by-step explanation:

The area, A of a regular hexagon can be obtained using the relation :

A = √3(p²/24)

The perimeter, p = 150 m

Therefore,

A = √3(150²/24)

A = √3(22500/24)

A = √3(937.5)

A = 1623.7976

A = 1623.80 m²

A = √3(1875/2) m²

Select the correct answer.

If function f has zeros at -3 and 4, which graph could represent function f?

A.
the graph of a quadratic function y = (1/4)(x+3)(x-4)
B.
the graph of a quadratic function y = -(1/4)(x-3)(x+4)
C.
the graph of a quadratic function y = -(x+3)(x+4)
D.
the graph of a quadratic function y = (x-3)(x-4)

Answers

A is valid
It is the only option where y(-3) and y(4) are both zero

Describe how you would factor x^2 + 10x - 24. Be specific.

Answers

Answer:

if u have more doubts feel free to ask :)

Step-by-step explanation:

x² + 10x -24  

x² + 12x - 2x - 24          

x(x + 12) -2(x + 12)

(x + 12) (x - 2)

Factors of 24 : ±1 , ±2 , ±3 , ±4 , ±6 , ±8 , ±12,  ±24. Combination of +12 and -2 gives "10" the middle term also " 24"

Solve the equation for x.

Answers

Answer:

x = 7

Step-by-step explanation:

2x + 34 = 4x + 20

2x = 14

x = 7

Please help if you answer and some extra points!

Answers

Answer: if you go to symbolab it will definitely help you and yes i know i did not help whatsoever but just try it if not im sorry

Step-by-step explanation:

6. A metal is made from copper, zinc and lead in the ratio 13:6:1
respectively. The mass of zinc is 90kg. Calculate the mass of the
metal. ​

Answers

Given:

A metal is made from copper, zinc and lead in the ratio 13:6:1.

The mass of zinc is 90kg.

To find:

The mass of the metal.

Solution:

It is given that the metal is made from copper, zinc and lead in the ratio 13:6:1.

Let the mass of copper, zinc and lead are 13x, 6x and 1x respectively.

The mass of zinc is 90kg. So,

[tex]6x=90[/tex]

[tex]x=\dfrac{90}{6}[/tex]

[tex]x=15[/tex]

Now, total mass of the metal is:

[tex]Total=13x+6x+1x[/tex]

[tex]Total=20x[/tex]

[tex]Total=20(15)[/tex]

[tex]Total=300[/tex]

Therefore, the mass of the metal is 300kg.

What is the measure of <JHM

25
45
50
90​

Answers

45 of course because it measured higher then others and it’s the systems of odd numbers

help pls. cant figure it out

Answers

Answer:

m=3

Step-by-step explanation:

add the m on the right side, 4m+3=15

subract the 3 on the left side, 4m=12

divide by four to isolate m, m=3

Answer:

[tex]3m+3=15-m[/tex]

[tex]3m+3=-m+15[/tex]

[tex]3m+m=15-3[/tex]

[tex]4m=12[/tex]

[tex]Divide\ both\ sides \ by\ 4[/tex]

[tex]\frac{4m}{4} =\frac{12}{4}[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{m=3}}}}}[/tex]

-------------------------hope it helps...have a great day!!

An equilateral triangle with side length 20 cm is shown in the diagram, work out the area of the triangle.Give your answer rounded to 1 DP.

Answers

Answer:

173.2 cm²

Step-by-step explanation:

Use the equilateral triangle area formula, A = [tex]\frac{\sqrt{3}}{4}[/tex]

Plug in the side length and solve:

A = [tex]\frac{\sqrt{3}}{4}[/tex]a²

A = [tex]\frac{\sqrt{3}}{4}[/tex](20)²

A = [tex]\frac{\sqrt{3}}{4}[/tex](400)

A = 173.2

So, the area of the triangle is approximately 173.2 cm²

Can anyone solve this question for me urgent! With work please. Thank you!

Answers

Answer:

P = 75*

Step-by-step explanation:

pleaseee helppp meeee!!!!

Answers

5x - 10 = 25 so first you have to add ten to both sides
5x-10=25
+10 +10
5x = 35
Then you divide both sides by 5
/5 /5
X = 7
And that’s how you get it!!

figure B is a scaled copy of figure A. What is the scale factor from figure A to B​

Answers

The scale factor from Figure A to Figure B is
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is the scale factor
Let
z-----> the scale factor
In this problem

substitute values

the scale factor is less than 1
therefore
is a reduction

The 5th grade teacher ordered 32 pizzas for an end-of-year celebration for their students.

-Each pizza was cut into equal sized slices.
-Each slice was 1/8 of a pizza.
How many slices of pizza were there in all?

Answers

Answer:

256

Step-by-step explanation:

There were 32 pizzas cut into 8 slices, so multiply the number of slices per pizza by the number of pizzas.

What is the 30th term of the linear sequence below?
-4,-1,2,5,8...

Answers

Answer:

80

Step-by-step explanation:

-4,-1,2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56,59,62,65,68,71,74,77,80.

7th grade math help me pleaseeee

Answers

Answer:

Step-by-step explanation:

the first one is a negative correlation

check the above for first

How do I solve and what's the answer?

Answers

Answer:

Step-by-step explanation:

A parallelogram is a family of quadrilateral which has its two opposite sides to be equal and parallel.

In the given parallelogram, the following proof can be deduced.

1. QS bisects RT: <RSQ ≅ <TQS                    Given

2. RV ≅ TV                                                      Definition of a bisector

3. <SRQ + < RQT = [tex]180^{o}[/tex]                                  Definition of supplementary angles

4. <RQS ≅ <QST                                             Definition of alternate angles

5. <RVT ≅ <QVT                                             Vertically opposite angles

6. <QRS ≅ <STQ                                             Opposite angles are congruent

7. QRST is a parallelogram                             Proofed

can someone assist me with this, has me mad
drop menu 1:
A. y-axis
B. x-axis
C. line y=x
D. line y=-x
drop menu 2:
A. 4 units to the right and 10 units up
B. 8 units to the right and 4 units up
C. 10 units to the right and 2 units up
D. 10 units to the right and 4 units up​

Answers

Answer:

A. y-axis

B. x-axis

C. line y=x

D. line y=-x

drop menu 2:

A. 4 units to the right and 10 units up

B. 8 units to the right and 4 units up

C. 10 units to the right and 2 units up

D. 10 units to the right and 4 units up​

Answer:

C, and D

Step-by-step explanation:

First you reflect over the line y=x (line goes diagonal from quadrant I to quadrant III)

The rule of reflecting over the y=x line is that point (x,y) becomes point (y,x)

For example, point C ( -4, 2), becomes C' ( 2, -4)

Second is a translation 10 units to the right and 4 units up from C'(2,-4) to C''(0, 12)

x- (-3) is the same as x + (-3).
O True
O False

Answers

Answer:

false

Step-by-step explanation:

because x - (-3)

= x+3

and x + - 3

= x - 3

so they are not the same

hope this helps

Answer:

False

Step-by-step explanation:

If u minus you go the opposite direction

And you have negative 3

So you do the opposite direction of -3 which is +3

So x+3

put 0.6 as a percent

Answers

Answer:

6%

Step-by-step explanation:

What are the solution(s) to the quadratic equation 50 – X2 = 0?
[tex]2 \sqrt{5} [/tex]
[tex] 6\sqrt{3} [/tex]
no real solution​

Answers

Answer:

Step-by-step explanation:

50 - x² = 0

50 = x²

x² = 50

x = √50

[tex]x = \sqrt{2*5*5}\\\\x=5\sqrt{2}[/tex]

Answer:

[tex]50 - {x}^{2} = 0 \\ {x}^{2} = 50 \\ x = \sqrt{50} \\ x = 5 \sqrt{2} [/tex]

Can someone help me with this?

Answers

Answer:

(b)

Step-by-step explanation:

5 - 3tan3x = 0 trên -π< x < π.

Answers

Answer:

x = 0.343

Step-by-step explanation:

We want to solve:

5 - 3tan(3x) = 0

such that:

-π< x < π

where π = 3.14

then:

-3.14 < x < 3.14

Let's solve the equation:

5 - 3tan(3x) = 0

-3tan(3x) = -5

tan(3x) = -5/-3 = 5/3

Now we can use the inverse tan function, Atan(x).

Remember that:

Atan( tan(x) ) = tan( Atan(x)) = x

Then if we apply that function to both sides, we get:

Atan( tan(3x)) = Atan(5/3)

3x = Atan(5/3)

x = Atan(5/3)/3 = 0.343

can someone please help me i need to calculate the are of a trapezium which is 6cm 15cm 9cm, please help

Answers

Answer:

Step-by-step explanation: The parallel sides of a trapezium are called the bases and the distance between them is the height. Therefore if 6cm and 15cm are the bases and 9cm is the height, then the area is A= ½(b1+b2)×h, where b1 is 6cm and b2 is 15cm and h is 9cm. Therefore the Area= ½(6+15)×9=94,5cm.

Answer:

shush its hard like my

Step-by-step explanation:

Which is true regarding chords and diameters of circles?

Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle.
Both chords and diameters have two endpoints on a circle. Chords must intersect the center of a circle.
Chords have two endpoints on a circle. Diameters have one endpoint on a circle and one at the center.
Chords have one endpoint on a circle and one at the center. Diameters have two endpoints on a circle.

Answers

The state that is valid is

"Every diameter of a circle is also a chord because a chord of a circle is any line segment joining two points on the circumference of the circle."

What is a diameter

A diameter is a line that divides a circle into two halves, a diameter is also a chord

What is a Chord

A chord is a line that connects points on a circle, a chord is not a diameter because it does not divide a circle into two equal halves

Learn more about circles here:

https://brainly.com/question/10458894

What is 1/root 2
Give me that ans asap

Answers

Answer:

1/√2

Approximate numerical value

1/√2 = 0.707106781186548

---------------------------

Rationalize the denominator

(1/√2) * (√2 / √2) = √2 / 2

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