Answer:
True
Step-by-step explanation:
Which of the following is not true about the inverse of f (x) = = 3x+5
2
Answer Before defining the inverse of a function we need to have the right mental image of function.
Consider the function f(x) = 2x + 1. We know how to evaluate f at 3, f(3) = 2*3 + 1 = 7. In this section it helps to think of f as transforming a 3 into a 7, and f transforms a 5 into an 11, etc.
Now that we think of f as "acting on" numbers and transforming them, we can define the inverse of f as the function that "undoes" what f did. In other words, the inverse of f needs to take 7 back to 3, and take -3 back to -2, etc.
Let g(x) = (x - 1)/2. Then g(7) = 3, g(-3) = -2, and g(11) = 5, so g seems to be undoing what f did, at least for these three values. To prove that g is the inverse of f we must show that this is true for any value of x in the domain of f. In other words, g must take f(x) back to x for all values of x in the domain of f. So, g(f(x)) = x must hold for all x in the domain of f. The way to check this condition is to see that the formula for g(f(x)) simplifies to x.
g(f(x)) = g(2x + 1) = (2x + 1 -1)/2 = 2x/2 = x.
This simplification shows that if we choose any number and let f act it, then applying g to the result recovers our original number. We also need to see that this process works in reverse, or that f also undoes what g does.
f(g(x)) = f((x - 1)/2) = 2(x - 1)/2 + 1 = x - 1 + 1 = x.
Letting f-1 denote the inverse of f, we have just shown that g = f-1.
Definition:
Let f and g be two functions. If
f(g(x)) = x and g(f(x)) = x,
then g is the inverse of f and f is the inverse of g.
Exercise 1:
Return to Contents
Finding Inverses
Example 1. First consider a simple example f(x) = 3x + 2.
The graph of f is a line with slope 3, so it passes the horizontal line test and does have an inverse.
There are two steps required to evaluate f at a number x. First we multiply x by 3, then we add 2.
Thinking of the inverse function as undoing what f did, we must undo these steps in reverse order.
The steps required to evaluate f-1 are to first undo the adding of 2 by subtracting 2. Then we undo multiplication by 3 by dividing by 3.
Therefore, f-1(x) = (x - 2)/3.
Steps for finding the inverse of a function f.
Replace f(x) by y in the equation describing the function.
Interchange x and y. In other words, replace every x by a y and vice versa.
Solve for y.
Replace y by f-1(x).
Example 2. f(x) = 6 - x/2
Step 1 y = 6 - x/2.
Step 2 x = 6 - y/2.
Step 3 x = 6 - y/2.
y/2 = 6 - x.
y = 12 - 2x.
Step 4 f-1(x) = 12 - 2x.
Step 2 often confuses students. We could omit step 2, and solve for x instead of y, but then we would end up with a formula in y instead of x. The formula would be the same, but the variable would be different. To avoid this we simply interchange the roles of x and y before we solve.
Example 3. f(x) = x3 + 2
This is the function we worked with in Exercise 1. From its graph (shown above) we see that it does have an inverse. (In fact, its inverse was given in Exercise 1.)
Step 1 y = x3 + 2.
Step 2 x = y3 + 2.
Step 3 x - 2 = y3.
(x - 2)^(1/3) = y.
Step 4 f-1(x) = (x - 2)^(1/3).
Exercise 3:
Graph f(x) = 1 - 2x3 to see that it does have an inverse. Find f-1(x). Answer
Step-by-step explanation:
pls brain list
. The industrial output of an automobile factory increases by 5% of what it had been in the beginning of
every year. Find the production after 3 years, if the factory turns out 80000 units this year.
Triangle XYZ with vertices X (1,-2) Y (3,-5) and Z (4,1) translated 5 units left and 3 units up
Answer:
x= (4,-7)
y= (6,-10)
z= (7,-4)
Step-by-step explanation:
Use the Distributive Property to determine which of the following statements is equivalent to 5(6 – 2).
What type of transformation transforms (a, b) to (-a, b)?
a reflection over the y-axis
a translation of 1 unit down
a reflection over the x-axis
a translation of 1 unit up
Answer:
A reflection over the y axis .
Step-by-step explanation:
Given : Transforms (a,b) to (-a,b).
To find : What type of transformation.
Solution : We have given
Parent function : (a,b) .
Transformed : (-a ,b).
Transformation rule of reflection over y axis : ( x, y) →→ ( -x ,y).
Then we can say in transformation (a,b) →→→→ (-a,b).
Therefore, A reflection over the y axis
Step-by-step explanation:
plz brain list
Answer:
hes right i took the test
Step-by-step explanation:
A submarine descended 3/4 of a kilometer in 1/4 of an hour. What was the submarine's rate of descent?
is this the right answer?
1 A lawnmower that regularly sells for $200 is on sale for $85. Find the % of change that the price was decreased by ??? percent. Round to the nearest whole percent.
Answer:
The price changed by 92.5 %
Step-by-step explanation:
The regular price of lawn mover = 200 dollars
The new selling price = 85 dollars
Change in selling price = 200 -85 dollars = 115 dollars
% change == [tex]\frac{185}{200} * 100 = 92.5[/tex]
The price changed by 92.5 %
367589+667556755788654578645
Answer: 667556755788655000000
Step-by-step explanation: braniliest pls
Add the fractions. Reduce the answer to lowest terms.
8\9+1/9
Answer:
1
Step-by-step explanation:
8 + 1 = 9/9
- -
9. 9
If you monthly salary is 5,167 and 28% is withheld for taxes and social security. How much money will be withheld from your check?
Answer:
jjjjjjj
Step-by-step explanation:
nnnnnnn
Paul got 15 out of 20 questions correct on his test. What percent of the questions did Paul get correct?
Answer:75%
Step-by-step explanation:
To make a fraction into a percent you have to multiply it by 100
So: 15/20 x 100=15x5=75 so he got 75% of his problems right
please hurry. 1. Calculate the grade point average: An A is considered 4.0, a B is 3.0, a C is 2.0, a D is 1.0, and an F is 0. If you received the following grades, what would be your grade point average? Round your answer to the hundredths place. Please show me how you got ur answer step by step
Course Credits Grade
Sociology 3.0 A
Calculus 4.0. F
New Student Seminar 1.0 C
Physics. 5.0. A
Answer:
b
Step-by-step explanation:
URGENT NEED ANSWERS •_•
Can someone give me the answer asap
Answer:
https://brainly.in/...,..,
Answer:
38.4895cm²
Step-by-step explanation:
area of a circle with r=7
3.142×7² = 153.958
153.958/4 = 38.4895
Plzzzzzz help meeee plz I am timed
Answer:
multiplication property of equality. Hope this help and maybe a brainlist?
Step-by-step explanation:
Answer:
multiplication property of equality
Step-by-step explanation:
d/10=12
Multiply both sides by the equation by 10
10× d/10=10×12
Reduce the numbers by the greatest common factor which is 10
d=10×12
Multiply 10 and 12
d=120
So using multiplication to solve this equation
Please answer ASAP!
Which proportional relationship has the greatest rate of change?
Answer:
Option (1) ; y = 7x
Step-by-step explanation:
(1) reads y = 7x, a line with slope 7, therefore the rate of change in this is 7
(2) says that y increases 12 units every time that x increases 4 Then the rate of change is: (increase in y / increase in x = 12/4 =3
(3) shows a table from which we can see that an increase of y in 8 corresponds to an increase of x in 2: rate of change = (8 - 0) , (2 - 0) = 4
(4) shos a line with slope (rate of change) given by: (12 - 0) / (2 - 0) = 12/2 = 6
Therefore, the greatest rate of change is shown by the first expression
y = 7 x
4. A surgical patient needs to have her liquid intake carefully monitored. How many mL of fluid did she consume if she
drankL of water, a pint of milk, and 8 oz of juice?
What is - or how do you find answer to:
12 1/2 - (-4 1/2) =
Answer:
8
Step-by-step explanation:
12 times 1/2=6
(-4(1/2))= -2
6-(-2)
6+2
=8
72: 24 equivalent to?
3:1 is the answer
it is simplified
I need help once more (●'◡'●)
Answer:
3= 25 4= 20 25= 5
Step-by-step explanation:
its a pattern. the top goes up by ones and the bottom goes up by fives.
Roger made a table showing how he spent his time in one day. How many days
will go by before Rodger has slept the equivalent of one day. Explain how you found your answer!
Data:
work : 1/3 day
sleep : 3/8 day
meals: 1/8 day
computer : 1/6 day
PLSSS.... Answer must be whole #
Answer:
Roger will have to sleep 2.667 days.
Step-by-step explanation:
If Roger sleeps 3 / 8 of a day in one day.
Then for Roger to sleep the equivalent of one day he will have to sleep
=
a dog walks 696 steps in 12 minutes. how many steps in 12 minutes
Answer:
696 steps
Step-by-step explanation:
the graph of a system of linear equation is shown below
Answer:
B
Step-by-step explanation:
What's the place value of 3 in 19.364?
Answer:
Tenths
Hope this helps :)
Answer:
tenths
Step-by-step explanation:
You and some friends are at a Chinese restaurant. You order several `\$2.00` plates of wontons. Your bill is `\$24`. How many plates of wontons did you order?
Answer:
12
Step-by-step explanation:
It does not say what the tax is so the answer would be 12. You just divide 2 by 24.
Answer:
12
Step-by-step explanation:
24 divided by 2 is 12 or 2 times 12 is 24
mark me brainliest
PLS HELP!!!! :))) BDHDHSJWJDJD
Answer:
Your answer is "H"
Step-by-step explanation:
The equation w(t)=100+40t models the weight (w(t) in grams) of a male white laboratory rat t weeks after its birth.
What is the rate of change? What does it mean in the context of the problem?
What is the y-intercept? What does it represent in the context of the problem?
Answer:
Step-by-step explanation:
Lacy is given a kite with one diagonal....please click photo to see the question
Answer:
the choice shown is correct. A reflection across diagonal BD.
Step-by-step explanation:
Answer:
your right, its A.
Step-by-step explanation:
An 180 rotation would result it with point C being below point A, not making it congruent. A translation is also not possible. A dilation would do nothing. A relfection on the other hand, would make both sides congruent.
The value, y, in dollars of an autographed basketball after x years can be represented by the function y=4000(1.05)x.
What is the value of the basketball after 5 years to the nearest dollar?
Answer:
I took the test!!
Step-by-step explanation:
Pit this in your calculator exactly like this 4,000(1.05)^5 and you get the answer 5,105.12625. So round your answer to the nearest dollar, which is 5,105.
