Question

Simplifique f(x+h) - f(x)/h sendo f(x) igual a :
a) 2x+1
b)3x-8
c) -2x+4

Answer 1

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

b)
$\boxed{f(x)=3x-8}\\ \\ \frac{f(x+h)-f(x)}{h}=\frac{3(x+h)-8-(3x-8)}{h}=\frac{3x+3h-8-3x+8}{h}=\frac{3h}{h}=3$

c)
$\boxed{f(x)=-2x+4}\\ \\ \frac{f(x+h)-f(x)}{h}=\frac{-2(x+h)+4-(-2x+4)}{h}=\frac{-2x-2h+4+2x-4}{h}=\frac{-2h}{h}=-2$