Question

let $f(x) = -2x + 6$ and $g(x) = 5x - 7$
find $f + g$.
a. $3x + 13$
b. $3x - 1$
c. $7x - 1$
d. $-10x - 35$

Explanation:

Step1: Recall the definition of function addition

To find \( f + g \), we use the formula \( (f + g)(x)=f(x)+g(x) \).

Step2: Substitute the given functions

Given \( f(x)=-2x + 6 \) and \( g(x)=5x - 7 \), we substitute these into the formula:
\( (f + g)(x)=(-2x + 6)+(5x - 7) \)

Step3: Combine like terms

First, combine the \( x \)-terms: \( -2x+5x = 3x \)
Then, combine the constant terms: \( 6 - 7=-1 \)
So, \( (f + g)(x)=3x - 1 \)

Answer:

B. \( 3x - 1 \)