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Chapter 5: Q 7. (page 267)

If f is a one-to-one function and $f (3) = 8$ , then $f^{- 1} (8) =$ $\dots \dots$

Short Answer

Expert verified

if $f$ is a one-to-one function and $f (3) = 8$ , then $f^{- 1} (8) = 3$

Step by step solution

01

Step 1. Definition of inverse function

An inverse function is a function that returns the original value for which a function has given the output. If $f (x)$ is a function which gives output $y$ , then the inverse function of $y$ , i.e. $f^{- 1} (y)$ will return the value $x$ .

02

Step 2. Explanation

Given that $f$ is one-to-one function and $f (3) = 8$ .

Then according to definition of inverse function $f^{- 1} (8) = 3$ .

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Most popular questions from this chapter

the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{x^{2} - 4}{2 x^{2}} x > 0$

If $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 23.

Vehicle Stopping Distance Taking into account reaction time, the distance $d$ (in feet) that a car requires to come to a complete stop while traveling $r$ miles per hour is given by the function

localid="1646198784356" $d (r) = 6.97 r - 90.39$

a. Express the speed $r$ at which the car is traveling as a function of the distance localid="1646198792401" $d$ required to come to a complete stop

b. Verify that localid="1646198797631" $r = r (d)$ is the inverse of localid="1646198802104" $d = d (r)$ by showing that localid="1646198806352" $r (d (r)) = r$ and localid="1646198811055" $d (r (d)) = d$

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" $300$ feet.

$d (r (d)) = d$

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False

To graph ${(x - 2)}^{3}$ , shift the graph of $y = x^{3}$ to the left $2$ units.

solve each equation. Verify your results using a graphing utility.

$5^{x^{2} + 8} = 125^{2 x}$

See all solutions

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