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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 19. (page 256)

Find for the given functions $f, g$ such that
$f (x) = \frac{3}{x + 1}, g (x) = x^{\frac{1}{3}}$ .
Find : (a) $(f 鈭� g) (4)$ (b) $(g 鈭� f) (2)$ (c) $(f 鈭� f) (1)$ (d) $(g 鈭� g) (0)$ .

Short Answer

Expert verified

The values are : (a) $\frac{3}{2^{\frac{2}{3}} + 1}$ (b) $1$ (c) $\frac{6}{5}$ (d) 0.

Step by step solution

01

Part (a) Step 1. Given Information

The given functions are :

$f (x) = \frac{3}{x + 1}, g (x) = x^{\frac{1}{3}}$ .

02

Part (a) Step 2. The Evaluation of a functional value.

The functional value are :

(a) $(f 鈭� g) (4) = f (g (4)) = f (2^{\frac{2}{3}}) = \frac{3}{2^{\frac{2}{3}} + 1}$ .

(b) localid="1646903360151" $(g 鈭� f) (2) = g (f (2)) = g (1) = 1$ .

(c) localid="1646903381376" $(f 鈭� f) (1) = f (f (1)) = f (\frac{3}{2}) = \frac{6}{5}$ .

(d)localid="1646903405090" $(g 鈭� g) (0) = g (g (0)) = g (0) = 0$ .

03

Part (b) Step 1. Given Information.

The given function be

$f (x) = \frac{3}{x + 1}, g (x) = x^{\frac{1}{3}}$ .

04

Part (b) Step 2. Evaluation of a functional value.

The functional value be

$(g 鈭� f) (2) = g (f (2)) = g (1) = 1$ .

05

Part (c) Step 1. Given Information.

The given function be

$f (x) = \frac{3}{x + 1}, g (x) = x^{\frac{1}{3}}$ .

06

Part (c) Step 2. Evaluation of a functional value.

The functional value be

$(f 鈭� f) (1) = f (f (1)) = f (\frac{3}{2}) = \frac{6}{5}$ .

07

Part (d) Step 1. Given Information.

The given function be

$f (x) = \frac{3}{x + 1}, g (x) = x^{\frac{1}{3}}$ .

08

Part (d) Step 2. Evaluation of a functional value.

The functional value be

$(g 鈭� g) (0) = g (g (0)) = g (0) = 0$ .

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Most popular questions from this chapter

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

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

If $f (x) = 3 x^{2} - 7$ and $g (x) = 2 x + a$ , find $a$ so that the graph of $f 鈭� g$ crosses the y-axis at 68.

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

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

Evaluate each expression using the values given in the table.

(a) $(f 鈭� g) (1)$ (b) $(f 鈭� g) (2)$ (c) $(g 鈭� f) (2)$ (d) $(g 鈭� f) (3)$ (e) $(g 鈭� g) (1)$ (f) $(f 鈭� f) (3)$ .

Solve the equation $3^{- x} = 81$

and verify your results using a graphing utility.

See all solutions

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