Question

type your answer and then click or tap done.
use the ^ symbol (shift+6 on the keyboard) to signify an exponent. for example, for 2 to the third power, enter 2^3.
the domain for f(x) and g(x) is the set of all real numbers.
let f(x) = 5x^2 - 4x and g(x) = 5x + 1.
find f + g.
guided practice
definition\tfunction operations
addition\t(f + g)(x) = f(x) + g(x)
multiplication\t(f • g)(x) = f(x) • g(x)
subtraction\t(f - g)(x) = f(x) - g(x)
division\t\\(\left(\frac{f}{g}\
ight)(x) = \frac{f(x)}{g(x)}, g(x) \
eq 0\\)

Explanation:

Step1: Recall the formula for function addition

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

Step2: Substitute the given functions

We know that \( f(x) = 5x^2-4x \) and \( g(x)=5x + 1 \). Substitute these into the formula:
\( (f + g)(x)=(5x^2-4x)+(5x + 1) \)

Step3: Combine like terms

First, remove the parentheses: \( 5x^2-4x + 5x + 1 \). Then, combine the like terms \(-4x\) and \(5x\):
\( 5x^2+(-4x + 5x)+1=5x^2+x + 1 \)

Answer:

$5x^2 + x + 1$