Question

function operations
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) = 5x² - 4x and g(x) = 5x + 1.
find f + g.
guided practice
definition\tfunction operations
\t(f + g)(x) = f(x) + g(x)
\t(f • g)(x) = f(x) • g(x)
\t(f - g)(x) = f(x) - g(x)
\t(\frac{f}{g})(x) = \frac{f(x)}{g(x)}, g(x) \
eq 0
addition\t
multiplication\t
subtraction\t
division\t

Explanation:

Step1: Recall function addition rule

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

Step2: Substitute the given functions

Given \( f(x) = 5x^{2}-4x \) and \( g(x)=5x + 1 \), substitute into the rule:
\( (f + g)(x)=(5x^{2}-4x)+(5x + 1) \)

Step3: Combine like terms

Combine the \( x \)-terms: \( -4x+5x = x \). The \( x^{2} \)-term and constant term remain as is. So we get \( 5x^{2}+x + 1 \).

Answer:

\( 5x^2 + x + 1 \)