Given `f(x) = ax^2` where a is constant, find f'(x) by definition. Hence find f'(2).

If ‘f' is defined by f(x) = x^2 , find f' (2).

if f'(x) = 3x^2-2/x^3 and f(1)=0 , find f(x).

Given f(x) = 2x^3 , find f'(x) by delta method.

Let A =R- {2} and B=R - {1}. If f ArarrB is a function defined by f(x) = (x-1)/(x-2) , show that f is one -one and onto, hence find f^(-1)

Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by f(x)= (x-2)/(x-3) show that f is one -one and onto, hence find f^(-1) .

If f'(x)=x^2-1/x^2 and f(1)=1/3 , find f(x).

If f'(x)=x/2 + 2/x and f(1)=5/4 , then find f(x) .

If f(x) = {:{(x-2, x 3):} then, find f(8)

Given f(x) = 3x – 1. Find: (i) f(-2) (ii) f(5)