Question

A Function f(x) is defined as: (x) = 2x -1 / x-3 then evaluate f-1(5).

Answer 1

Let y=f(x)=(2x-1)/(x-3). We need x in terms of y.

y(x-3)=2x-1, xy-3y=2x-1, xy-2x=3y-1, x(y-2)=3y-1, x=(3y-1)/(y-2).

Let x=g(y)=(3y-1)/(y-2). Therefore g(x)=(3x-1)/(x-2).

g(x) is the inverse of f(x) so can be written g(x)=f^-1(x)=(3x-1)/(x-2).

So f^-1(5)=(15-1)/(5-2)=14/3.

CHECK

f(14/3)=(2×14/3-1)/(14/3-3)=(28-3)/(14-9)=25/5=5, that is f(14/3)=5. So 14/3=f^-1(5).