Q. The inverse of the function f(x)=ax+b, x∈R is f-1(x)=8x-3.

Soln:

Here, f(x) = ax + b

Let y be the image of x under f, then

y = ax + b

x = (y-b)/a

Interchanging the role of x and y we get, 

y = (x-b)/a

f^-1(x) = (x-b)/a

from given f^-1(x) = 8x - 3

So, (x-b)/a = 8x - 3

or, x/a - b/a = 8x - 3

Equating the coefficient of x and constant term, we have

1/a = 8

a=1/8

and b/a=3

or, b/(1/8) = 3

Therefore, b=3/8 

Hence, a=1/8 and b=3/8 Ans.