If f(x)=4/2-x, find the f(a), f(a+h), and f(a+h)-f(a)/h, where h is not equal to 0.

Answer 1

Assume you mean:
f(x)=4/(2-x)
find the f(a), f(a+h), and
[ f(a+h)-f(a) ] /h
where h is not equal to 0.
f(a) = 4/(2-a)
f(a+h) = 4/(2-a-h)

f(a+h)-f(a) =4/(2-a-h)-4/(2-a)

= 4 [ (2-a) - (2-a-h)] /[ (2-a)(2-a-h)]

= 4 [ h / [4 -4a +a^2 +ah -2h ]
divide by h
4 [ 1 / [4 -4a +a^2 +ah -2h ] answer

***Notice that when h-->0 this becomes
4 [ 1 / [4 -4a +a^2 ]