Question

let F(x)=x-1/3x find f(a+h)-f(a)/h

sorry if this is difficult to understand.

Answer 1

f(x) = x - 1/3x ??

I think there are some missing brackets here, such as
f(x) = (x-1)/(3x) or some variation of that
or else why didn't they just say
f(x) = 2/3x ?

come back with the correction and I'll what I can do

Answer 2

yes sorry
let F(x)=(x-1)/(3x) find f(a+h)-f(a)/h.

f(x)=(x-1) over (3x) find f(a+h)-f(a) all over h.

Answer 3

ok then
f(a) = (a-1)/(3a)
f(a+h) = (a+h - 1)/(3(a+h))

(f(a+h)-f(a) )/h
= ( (a+h - 1)/(3(a+h)) - (a-1)/(3a) )/h
= ( a(a+h - 1) - (a+h)(a-1) )/(3a(a+h)) * 1/h
= (a^2 + ah - a - a^2 + a - ah + h)/(3a(a+h)) * 1/h
= h/(3a(a+h)) * 1/h
= 1/(3a(a+h))

Answer 4

I am confused by the multiplication of 1/h.