Question

let ( f(x) = 3x^2 - 2x + 6 ) and ( g(x) = 7x - 4 ). identify the rule for ( f + g ).
a ( 147x^2 - 182x + 62 )
b ( 3x^2 + 7x + 10 )
c ( 3x^2 + 5x + 2 )
d ( 3x^2 - 9x + 10 )

Explanation:

Step1: Recall the rule for adding functions

To find \( f(x) + g(x) \), we add the corresponding terms of \( f(x) \) and \( g(x) \). Given \( f(x)=3x^{2}-2x + 6 \) and \( g(x)=7x-4 \), we have:
\( f(x)+g(x)=(3x^{2}-2x + 6)+(7x-4) \)

Step2: Combine like terms

First, combine the \( x^{2} \) terms: \( 3x^{2} \) (since there is no \( x^{2} \) term in \( g(x) \)).
Then, combine the \( x \) terms: \( - 2x+7x = 5x \).
Finally, combine the constant terms: \( 6-4=2 \).
So, \( f(x)+g(x)=3x^{2}+5x + 2 \)

Answer:

C. \( 3x^{2}+5x + 2 \)