Saturday, August 12, 2017

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.