Question

If f(x) = 4^x-8 and g(x) = 5x+6, find (f + g)(x)

A. (F+g)(x) = -4^x - 5x + 2
B.(F+g)(x) = 4^x + 5x - 2
C.(F+g)(x) = 4^x - 3x + 6
D.(F+g)(x) = 9x - 2

Answer 1

Hey there!

We are given two functions - one is Exponential while the another one is Linear.

`\large{ \begin{cases} f(x) = {4}^(x) - 8 \\ g(x) = 5x + 6 \end{cases}}`

1. Operation of Function

• (f+g)(x) is a factored form of f(x)+g(x). We can common factor out x. Therefore:

`\large{(f + g)(x) = f(x) + g(x)}`

2. Substitution

• Next, we substitute f(x) = 4^x+8 and g(x) = 5x+6.

`\large{(f + g)(x) = ( {4}^(x) - 8) + (5x + 6)}`

3. Evaluate/Simplify

• Cancel out the brackets and combine like terms.

`\large{(f + g)(x) = {4}^(x) - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^(x) + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^(x) + 5x - 2}`

4. Final Answer

• (f+g)(x) = 4^x+5x-2