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Chapter 2: Q. 73 (page 69)

Given f(x)=3x+1and (f+g)(x)=6-12x, find the function g.

Short Answer

Expert verified

The value ofg(x)=5(1-3x)

Step by step solution

01

Step 1. Given Information

Givenf(x)=3x+1and(f+g)(x)=6-12x

We have to find the functiong.

02

Step 2. We know that (f+g)(x)=f(x)+g(x)Simplifying the formula for g(x)

Subtract f(x)on both side

(f+g)(x)-f(x)=f(x)+g(x)-f(x)(f+g)(x)-f(x)=g(x)g(x)=(f+g)(x)-f(x)

03

Step 3. Putting the value off(x) and (f+g)(x)

g(x)=6-12x-3x+1g(x)=6-12x-3x-1

Simplify

g(x)=6-12x-3x-1g(x)=5-15xg(x)=5(1-3x)

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