Chapter 2 - Section 2.8 - Function Operations and Composition - 2.8 Exercises - Page 268: 33

$a)$ $f(x+h)=2-x-h$ $b)$ $f(x+h)-f(x)=-h$ $c)$ $\frac{f(x+h)-f(x)}{h}=-1$

$a)$ $$f(x)=2-x$$ Replace $x$ with $x+h$: $$f(x+h)=2-(x+h)$$ $$f(x+h)=2-x-h$$ $b)$ $$f(x+h)-f(x)$$ Substitute corresponding expressions: $$2-x-h-(2-x)$$ $$2-x-h-2+x=-h$$ $c)$ $$\frac{f(x+h)-f(x)}{h}$$ Substitute corresponding expression for numerator: $$\frac{-h}{h}=-1$$