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Chapter 5: Q. 87 (page 270)

The function $f (x) = | x |$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .

Short Answer

Expert verified

The function and the inverse is

$f (x) = | x |, x \geq 0 f^{- 1} (x) = x, x \geq 0$

Step by step solution

Given information

Given the function $f (x) = | x |$

Calculating the inverse

The function is $f (x) = | x |$ . Replacing $f (x)$ with $y$ , we get

$f (x) = | x | y = x x = y f^{- 1} (x) = x (x \geq 0)$

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Most popular questions from this chapter

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.

$d (r (d)) = d$

Solve the equation $3^{x^{3}} = 9^{x}$

and verify your results using a graphing utility.

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

$9^{- x + 15} = 27^{x}$

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

localid="1646160286433" $f (x) = 5 - e^{- x}$

The function $f (x) = x^{4}$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .

See all solutions

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The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

Short Answer

Step by step solution

Given information

Calculating the inverse

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Most popular questions from this chapter

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The function $f (x) = | x |$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .