Question

given (f(x)=2x + 2). (a) find (f(x + h)) and simplify. (b) find (\frac{f(x + h)-f(x)}{h}) and simplify. part: 0 / 2 part 1 of 2 (a) (f(x + h)=)

Explanation:

Step1: Substitute \(x + h\) into \(f(x)\)

Given \(f(x)=2x + 2\), then \(f(x + h)=2(x + h)+2\).
Expand the expression: \(f(x + h)=2x+2h + 2\).

Step2: Calculate \(\frac{f(x + h)-f(x)}{h}\)

First, find \(f(x + h)-f(x)\). Since \(f(x + h)=2x+2h + 2\) and \(f(x)=2x + 2\), then \(f(x + h)-f(x)=(2x+2h + 2)-(2x + 2)=2h\).
So, \(\frac{f(x + h)-f(x)}{h}=\frac{2h}{h}=2\).

Answer:

(a) \(f(x + h)=2x+2h + 2\)
(b) \(\frac{f(x + h)-f(x)}{h}=2\)