Chapter 10: Q. 2 (page 1002)

In the following exercises, find
a. $f \circ g (x)$
b. $g \circ f (x)$
c. $(f . g) (x)$
$f (x) = 3 x - 1 g (x) = 5 x - 3$

Short Answer

Expert verified

The composition is $15 x - 10, 15 x - 8, 15 x^{2} - 14 x + 3$ respectively

Step by step solution

Given information

Given the function

$f (x) = 3 x - 1 g (x) = 5 x - 3$

Use the composition and calculate

Using composition, we get

$f \circ g (x) = f (5 x - 3) f \circ g (x) = 3 (5 x - 3) - 1 f \circ g (x) = 15 x - 9 - 1 f \circ g (x) = 15 x - 10$

Using composition and calculating

Using composition, we get

$g \circ f (x) = g [f (x)] g \circ f (x) = g (3 x - 1) g \circ f (x) = 5 (3 x - 1) - 3 g \circ f (x) = 15 x - 5 - 3 g \circ f (x) = 15 x - 8$

Using composition and calculate

Using composition, we get

$(f \cdot g) (x) = f (x) \cdot g (x) (f \cdot g) (x) = (3 x - 1) \cdot (5 x - 3) (f \cdot g) (x) = 15 x^{2} - 9 x - 5 x + 3 (f \cdot g) (x) = 15 x^{2} - 14 x + 3$

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In the following exercises, find
a. $f \circ g (x)$
b. $g \circ f (x)$
c. $(f . g) (x)$
$f (x) = 3 x - 1 g (x) = 5 x - 3$

Short Answer

Step by step solution

Given information

Use the composition and calculate

Using composition and calculating

Using composition and calculate

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In the following exercises, finda.f∘g(x)b.g∘f(x)c.(f.g)(x)f(x)=3x-1g(x)=5x-3

Short Answer

Step by step solution

Given information

Use the composition and calculate

Using composition and calculating

Using composition and calculate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Calculus

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Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, find
a. $f \circ g (x)$
b. $g \circ f (x)$
c. $(f . g) (x)$
$f (x) = 3 x - 1 g (x) = 5 x - 3$