Q. f(4x+5)=12x+18 , find the f'(x)

Soln:

Let 4x + 5 = a 

or, x = (a-5)/4

Then, 

f(a) = 12*(a - 5)/4 + 18

       = 3*(a - 5) + 18

       = 3a - 15 + 18

       = 3a + 3

Therefore, 

f(x) = 3x + 3

Let y = f(x)

or, y = 3x + 3

or, x = (y - 3)/3

Interchanging the role of x and y, we get,

y = (x - 3)/3

f^-1(x) = (x - 3)/3 Ans.