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Chapter 5: Q 10. (page 267)

True or False If $f$ and $g$ are inverse functions, the domain of $f$ is the same as the range of $g$ .

Short Answer

Expert verified

Its true, If $f$ and $g$ are inverse functions, the domain of $f$ is the same as the range of $g$ .

Step by step solution

Step 1. Given

Given that $f$ and $g$ are inverse function.

Step 2. Explanation

If $f (x)$ and $f^{- 1} (x)$ are inverse functions, then domain of $f (x)$ is same as the range of $f^{- 1} (x)$ .

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Most popular questions from this chapter

Use the graph of $y = f (x)$ given in Problem $44$ to evaluate

the following:

(a) $f (2)$

(b) $f (1)$

(d) $f^{- 1} (- 1)$

Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function

$W (h) = 50 + 2.3 (h - 60)$

(a) What is the ideal weight of a $6$ -foot male?

(b) Express the height has a function of weight W.

(c) Verify that $h = W (h)$ is the inverse of $W = W (h)$ by showing that role="math" localid="1646158219737" $h (W (h)) = h$ and $W (h (W)) = W$ .

(d) What is the height of a male who is at his ideal weight of $80$ kilograms?

[Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given byrole="math" localid="1646159253780" $W (h) = 45.5 + 2.3 (h - 60)$ .

Use transformations to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = 1 - 2^{- x / 3}$

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{2}{3 + x}$

If $f (x) = a x + b$ and $g (x) = c x + d$ , then find: -

(a) $f \circ g$

(b) $g \circ f$

(c)the domain of $f \circ g$ and $g \circ f$

(d)the conditions for which $f \circ g = g \circ f$

See all solutions

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True or False If fand gare inverse functions, the domain of f is the same as the range of g.

Short Answer

Step by step solution

Step 1. Given

Step 2. Explanation

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Most popular questions from this chapter

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True or False If $f$ and $g$ are inverse functions, the domain of $f$ is the same as the range of $g$ .