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Chapter 5: Q 1. Given Information (page 256)

Find $f (3 x)$ if $f (x) = 4 - 2 x^{2}$ .

Short Answer

Expert verified

The value of $f (3 x) = 4 - 18 x^{2}$ .

Step by step solution

01

Step 1. The calculation of the given functional value.

Substitute the value of $x = 3 x$ ,in the given function

role="math" localid="1646137279761" $\begin{array}{rcl} f (3 x) & = & 4 - 2 \times {(3 x)}^{2} \\ f (3 x) & = & 4 - 2 \times 9 x^{2} \\ f (3 x) & = & 4 - 18 x^{2} \end{array}$

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Most popular questions from this chapter

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

True or False

The domain of the exponential function

$f (x) = a^{x}$ where $a > 0, a \neq 1$ is the set of all real numbers.

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

$f (x) = - \frac{3 x + 1}{x}$

Solve the equation $5^{x} = 5^{- 6}$

and verify your results using a graphing utility

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

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

Height and Head Circumference. The head circumference

C of a child is related to the height H of the child (both in inches) through the function $H (C) = 2.15 C - 10.53$

(a) Express the head circumference C as a function of height H.

(b) Verify that $C = C (H)$ is the inverse of $H = H (C)$ by showing that $H (C (H)) = H$ and $C (H (C)) = C$ .

(c) Predict the head circumference of a child who is $26$ inches tall.

See all solutions

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