Question

find \\(f + g\\), \\(f - g\\), \\(fg\\) and \\(\frac{f}{g}\\). determine the domain for each function.

\\f(x) = 2x^2 - 17x + 36, \quad g(x) = x - 4\\

\\((f + g)(x) = \\) (simplify your answer.)

Explanation:

Define the functions and operation

Given:

$$ f(x) = 2x^2 - 17x + 36 $$

$$ g(x) = x - 4 $$

The sum operation is defined as:

$$ (f + g)(x) = f(x) + g(x) $$

Perform the addition

Substitute the expressions for \(f(x)\) and \(g(x)\):

$$ (f + g)(x) = (2x^2 - 17x + 36) + (x - 4) $$

Combine like terms

Group and simplify the terms:

$$ (f + g)(x) = 2x^2 + (-17x + x) + (36 - 4) $$

$$ (f + g)(x) = 2x^2 - 16x + 32 $$

Answer:

\((f + g)(x) =\) <blank>\(2x^2 - 16x + 32\)</blank> (Simplify your answer.)