Answer
$a)$ $f(x+h)=6x+6h+2$
$b)$ $f(x+h)-f(x)=6h$
$c)$ $\frac{f(x+h)-f(x)}{h}=6$
Work Step by Step
$a)$
$$f(x)=6x+2$$
Replace $x$ with $x+h$:
$$f(x+h)=6(x+h)+2$$
$$f(x+h)=6x+6h+2$$
$b)$
$$f(x+h)-f(x)$$
Substitute corresponding expressions:
$$6x+6h+2-(6x+2)$$
$$6x+6h+2-6x-2=6h$$
$c)$
$$\frac{f(x+h)-f(x)}{h}$$
Substitute corresponding expression for numerator:
$$\frac{6h}{h}=6$$
