given (f(x)=2x + 2). (a) find (f(x + h)) and simplify. (b) find (\frac{f(x + h)-f(x)}{h}) and simplify…

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)=)

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)=)

Answer

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)