Chapter 10: Q. 10.1 (page 991)

For functions $f (x) = 3 x - 2$ and
$g (x) = 5 x + 1$ , find
$(f \circ g) (x)$
$(g \circ f) (x)$
$(f \cdot g) (x)$

Short Answer

Expert verified

Part a. $(f \circ g) (x) = 15 x + 1$

Part b. $(g \circ f) (x) = 15 x - 9$

Part c. $(f \cdot g) (x) = 15 x^{2} - 7 x - 2$

Step by step solution

Part (a) Step 1. Find (f∘g)(x)

Using the definition of composition of functions $(f \circ g) (x) = f (g (x))$

Now substitute $5 x + 1$ for $g (x)$ .

$(f \circ g) (x) = f (5 x + 1)$

Find $f (5 x + 1)$ where $f (x) = 3 x - 2$ .

$(f \circ g) (x) = 3 (5 x + 1) - 2 (f \circ g) (x) = 15 x + 3 - 2 (f \circ g) (x) = 15 x + 1$

Part (b) Step 1. Find (g∘f)(x)

Using the definition of composition of function we have $(g \circ f) (x) = g (f (x))$ .

Now substitute $3 x - 2$ for $f (x)$ .

$(g \circ f) (x) = g (3 x - 2)$

Find $g (3 x - 2)$ where $g (x) = 5 x + 1$ .

$(g \circ f) (x) = 5 (3 x - 2) + 1 (g \circ f) (x) = 15 x - 10 + 1 (g \circ f) (x) = 15 x - 9$

Part (c) Step 1. Find (f·g)(x)

In this, we are multiplying the two functions. So we get

$(f \cdot g) (x) = f (x) \cdot g (x)$

Substitute $3 x - 2$ for $f (x)$ and $5 x + 1$ for $g (x)$ and simplify.

$(f \cdot g) (x) = (3 x - 2) (5 x + 1) (f \cdot g) (x) = 15 x^{2} + 3 x - 10 x - 2 (f \cdot g) (x) = 15 x^{2} - 7 x - 2$

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For functions $f (x) = 3 x - 2$ and
$g (x) = 5 x + 1$ , find
$(f \circ g) (x)$
$(g \circ f) (x)$
$(f \cdot g) (x)$

Short Answer

Step by step solution

Part (a) Step 1. Find (f∘g)(x)

Part (b) Step 1. Find (g∘f)(x)

Part (c) Step 1. Find (f·g)(x)

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For functions f(x)=3x-2andg(x)=5x+1, find(f∘g)(x)(g∘f)(x)(f·g)(x)

Short Answer

Step by step solution

Part (a) Step 1. Find (f∘g)(x)

Part (b) Step 1. Find (g∘f)(x)

Part (c) Step 1. Find (f·g)(x)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

For functions $f (x) = 3 x - 2$ and
$g (x) = 5 x + 1$ , find
$(f \circ g) (x)$
$(g \circ f) (x)$
$(f \cdot g) (x)$