Question

f(x) = x² - 3x + 5

g(x) = 2x² - 4x - 11

what is h(x) = f(x) + g(x)?

○ h(x) = 3x² - 7x - 6
○ h(x) = 2x² - 7x - 6
○ h(x) = -x² + x + 16
○ h(x) = 3x² - 7x - 11

Explanation:

Step1: Substitute the functions

Substitute \( f(x) = x^2 - 3x + 5 \) and \( g(x) = 2x^2 - 4x - 11 \) into \( h(x)=f(x)+g(x) \).
\( h(x)=(x^2 - 3x + 5)+(2x^2 - 4x - 11) \)

Step2: Combine like terms

Combine the \( x^2 \) terms: \( x^2+2x^2 = 3x^2 \)
Combine the \( x \) terms: \( -3x-4x=-7x \)
Combine the constant terms: \( 5 - 11=-6 \)
So, \( h(x)=3x^2-7x - 6 \)

Answer:

\( h(x) = 3x^2 - 7x - 6 \) (the first option: \( h(x)=3x^2 - 7x - 6 \))