Chapter 10: Q. 10.2 (page 991)

For functions $f (x) = 4 x - 3$ and
$g (x) = 6 x - 5$ , find
$(f \circ g) (x)$
$(g \circ f) (x)$
$(f \cdot g) (x)$

Short Answer

Expert verified

Part a. $(f \circ g) (x) = 24 x - 23$

Part b. $(g \circ f) (x) = 24 x - 23$

Part c. $(f \cdot g) (x) = 24 x^{2} - 38 x + 15$

Step by step solution

Part (a) Step 1. Find (f∘g)(x)

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

Now substitute $6 x - 5$ for $g (x)$ .

$(f \circ g) (x) = f (6 x - 5)$

Find $f (6 x - 5)$ where $f (x) = 4 x - 3$ .

$(f \circ g) (x) = 4 (6 x - 5) - 3 (f \circ g) (x) = 24 x - 20 - 3 (f \circ g) (x) = 24 x - 23$

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 $4 x - 3$ for $f (x)$ .

$(g \circ f) (x) = g (4 x - 3)$

Find $g (4 x - 3)$ where $g (x) = 6 x - 5$ .

$(g \circ f) (x) = 6 (4 x - 3) - 5 (g \circ f) (x) = 24 x - 18 - 5 (g \circ f) (x) = 24 x - 23$

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 $4 x - 3$ for $f (x)$ and $6 x - 5$ for $g (x)$ and simplify.

$(f \cdot g) (x) = (4 x - 3) (6 x - 5) (f \cdot g) (x) = 24 x^{2} - 20 x - 18 x + 15 (f \cdot g) (x) = 24 x^{2} - 38 x + 15$

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For functions $f (x) = 4 x - 3$ and
$g (x) = 6 x - 5$ , 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)=4x-3andg(x)=6x-5, 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

Pure Maths

Applied Mathematics

Mechanics Maths

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

For functions $f (x) = 4 x - 3$ and
$g (x) = 6 x - 5$ , find
$(f \circ g) (x)$
$(g \circ f) (x)$
$(f \cdot g) (x)$