Chapter 10: Q. 8 (page 1002)

In the following exercises, find
a. $f \circ g (x)$
b. $g \circ f (x)$
c. $(f . g) (x)$

Short Answer

Expert verified

The composition is $4 x^{2} - 13, = 16 x^{2} + 24 x + 5, 4 x^{3} - 16 x + 3 x^{2} - 12$ respectively

Step by step solution

Given information

Given the function

$f (x) = 4 x + 3 g (x) = x^{2} - 4$

Use the composition and calculate

Using composition, we get

$f \circ g (x) = f [g (x)] f \circ g (x) = f (x^{2} - 4) f \circ g (x) = 4 (x^{2} - 4) + 3 f \circ g (x) = 4 x^{2} - 16 + 3 f \circ g (x) = 4 x^{2} - 13$

Using composition and calculate

Using composition, we get

$g \circ f (x) = g [f (x)] g \circ f (x) = g (4 x + 3) g \circ f (x) = {(4 x + 3)}^{2} - 4 g \circ f (x) = 16 x^{2} + 9 + 24 x - 4 g \circ f (x) = 16 x^{2} + 24 x + 5$

Using the composition and calculate

Using composition, we get

$(f . g) (x) = f (x) . g (x) (f . g) (x) = (4 x + 3) \cdot (x^{2} - 4) (f . g) (x) = 4 x^{3} - 16 x + 3 x^{2} - 12$

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In the following exercises, find
a. $f \circ g (x)$
b. $g \circ f (x)$
c. $(f . g) (x)$

Short Answer

Step by step solution

Given information

Use the composition and calculate

Using composition and calculate

Using the composition and calculate

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Short Answer

Step by step solution

Given information

Use the composition and calculate

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Using the composition and calculate

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, find
a. $f \circ g (x)$
b. $g \circ f (x)$
c. $(f . g) (x)$