Chapter 10: Q. 5 (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 $6 x^{2} - 9 x, 18 x^{2} - 9 x, 6 x^{3} - 9 x^{2}$ respectively

Step by step solution

Given information

Given the function

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

Use the composition and calculate

Using composition, we get

$f \circ g (x) = f [g (x)] f \circ g (x) = f (2 x^{2} - 3 x) f \circ g (x) = 3 (2 x^{2} - 3 x) f \circ g (x) = 6 x^{2} - 9 x$

Use composition and calculate

Using composition, we get

$g \circ f (x) = g [f (x)] g \circ f (x) = g (3 x) g \circ f (x) = 2 {(3 x)}^{2} - 3 (3 x) g \circ f (x) = 18 x^{2} - 9 x$

Use composition and calculate

Using composition, we get

$(f . g) (x) = f (x) . g (x) (f . g) (x) = (3 x) \cdot (2 x^{2} - 3 x) (f . g) (x) = = 3 x \cdot 2 x^{2} - 3 x \cdot 3 x (f . g) (x) = 6 x^{3} - 9 x^{2}$

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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

Use composition and calculate

Use composition and calculate

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Short Answer

Step by step solution

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Use 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. $(f . g) (x)$