Question

question 6 of 10
if $f(x)=3x - 2$ and $g(x)=x^2 + 1$, find $(f + g)(x)$.

a. $2x + 3$

b. $x^2 + 3x + 1$

c. $x^2 + 3x - 1$

d. $4x^2 - 1$

Explanation:

Step1: Recall the definition of function addition

The sum of two functions \((f + g)(x)\) is defined as \(f(x)+g(x)\).

Step2: Substitute the given functions

We know that \(f(x) = 3x - 2\) and \(g(x)=x^{2}+1\). So, \((f + g)(x)=f(x)+g(x)=(3x - 2)+(x^{2}+1)\).

Step3: Simplify the expression

Remove the parentheses: \(3x - 2+x^{2}+1\). Then combine like terms: \(x^{2}+3x+( - 2 + 1)=x^{2}+3x - 1\).

Answer:

C. \(x^{2}+3x - 1\)