Chapter 2 - Graphs and Functions - 2.8 Function Operations and Composition - 2.8 Exercises - Page 288: 43

$\color{blue}{\bf{(a) 2-x-h }}$ $\color{blue}{\bf{(b) -h }}$ $\color{blue}{\bf{(c) -1 }}$

We are given the function: $\bf{f(x)= 2-x }$ $\bf{(a)}$ We are asked to find $f(x+h)$ $2- (x+h) $ $\color{blue}{\bf{ 2-x-h }}$ $\bf{(b)}$ We are asked to find $f(x+h)-f(x)$ $2-x-h-(2-x)$ $2-x-h-2+x$ $\color{blue}{\bf{ -h }}$ $\bf{(c)}$ We are asked to find $\dfrac{f(x+h)-f(x)}{h}$ $\dfrac{ -h }{h}$ $\color{blue}{\bf{ -1 }}$