Question

for the given functions f and g, complete parts (a)-(h).

\\(f(x) = 4x + 1\\); \\(g(x) = 2x - 7\\)

part 1 of 12

(a) find \\((f + g)(x)\\).

\\((f + g)(x) =\\) (simplify your answer. do not factor.)

Explanation:

Identify the given functions

We are given two functions:

$$f(x) = 4x + 1$$

$$g(x) = 2x - 7$$

State the definition of function addition

To find the sum of two functions, we use the definition of Function Addition:

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

Substitute the function expressions

Substitute the given expressions for \(f(x)\) and \(g(x)\) into the addition formula:

$$(f + g)(x) = (4x + 1) + (2x - 7)$$

Combine like terms

Group the variable terms and the constant terms together:

$$(f + g)(x) = (4x + 2x) + (1 - 7)$$

$$(f + g)(x) = 6x - 6$$

Answer:

(a) Find \((f + g)(x)\).

\((f + g)(x) =\) <blank>\(6x - 6\)</blank> (Simplify your answer. Do not factor.)