Chapter 5: Q. 5 (page 348)

In Problems 5–7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.
$f (x) = 2 - x g (x) = 3 x + 1$

Short Answer

Expert verified

$(f o g) (x) = 1 - 3 x D o m a i n : A l l r e a l n u m b e r s (g o f) (x) = 7 - 3 x D o m a i n : A l l r e a l n u m b e r s (f o f) (x) = x D o m a i n : a l l r e a l n u m b e r s (g o g) (x) = 9 x + 4 D o m a i n : a l l r e a l n u m b e r s$

Step by step solution

Given Information

Given two functions are

$f (x) = 2 - x g (x) = 3 x + 1$

Part(a): Step 1 : composition of functions

$f (x) = 2 - x g (x) = 3 x + 1 (f o g) (x) = f (g (x)) = f (3 x + 1) = 2 - (3 x + 1) = - 3 x + 1 (f o g) (x) = - 3 x + 1$

Domain is all real numbers

Part(b) : Step 1 : composition of functions

$f (x) = 2 - x g (x) = 3 x + 1 (g o f) (x) = g (f (x)) = g (2 - x) = 3 (2 - x) + 1 = 7 - 3 x (g o f) (x) = 7 - 3 x D o m a i n : A l l r e a l n u m b e r s$

Part(c): Step 1: composition of functions

$f (x) = 2 - x g (x) = 3 x + 1 (f o f) (x) = f (f (x)) = f (2 - x) = 2 - (2 - x) = + x (f o f) (x) = x D o m a i n : A l l r e a l n u m b e r s$

Part(d): Step 1: composition of functions

$f (x) = 2 - x g (x) = 3 x + 1 (g o g) (x) = g (g (x)) = g (3 x + 1) = 3 (3 x + 1) + 1 = 9 x + 4 (g o g) (x) = 9 x + 4 d o m a i n : A l l r e a l n u m b e r s$

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In Problems 5–7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.
$f (x) = 2 - x g (x) = 3 x + 1$

Short Answer

Step by step solution

Given Information

Part(a): Step 1 : composition of functions

Part(b) : Step 1 : composition of functions

Part(c): Step 1: composition of functions

Part(d): Step 1: composition of functions

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In Problems 5–7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.f(x)=2-xg(x)=3x+1

Short Answer

Step by step solution

Given Information

Part(a): Step 1 : composition of functions

Part(b) : Step 1 : composition of functions

Part(c): Step 1: composition of functions

Part(d): Step 1: composition of functions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Statistics

Geometry

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 5–7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.
$f (x) = 2 - x g (x) = 3 x + 1$