Chapter 10: Q. 3 (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 $24 x + 1, 24 x - 19, 24 x^{2} - 14 x - 5$ respectievly

Step by step solution

Given information

Given the function

$f (x) = 6 x - 5 g (x) = 4 x + 1$

Use the composition and calculate

Using the composition, we get

$f \circ g (x) = f [g (x)] f \circ g (x) = f (4 x + 1) f \circ g (x) = 6 (4 x + 1) - 5 f \circ g (x) = 24 x + 6 - 5 f \circ g (x) = 24 x + 1$

Using the composition and calculate

Using the composition, we get

$g \circ f (x) = g [f (x)] g \circ f (x) = g (6 x - 5) g \circ f (x) = 4 (6 x - 5) + 1 g \circ f (x) = 24 x - 20 + 1 g \circ f (x) = 24 x - 19$

Use the composition and calculate

Using composition, we get

$(f \cdot g) (x) = f (x) \cdot g (x) (f \cdot g) (x) = (6 x - 5) \cdot (4 x + 1) (f . g) (x) = 24 x^{2} + 6 x - 20 x - 5 (f . g) (x) = 24 x^{2} - 14 x - 5$

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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 the composition and calculate

Use the composition and calculate

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a. $f \circ g (x)$
b. $g \circ f (x)$
c. $(f . g) (x)$