Find the inverse of fx 25xSolutionTo find f1x Let fx y fx

Find the inverse of f(x) = 2/(5-x)

Solution

To find f^-1(x) ,

Let f(x) = y

f(x) = 2/(5-x) =y ------>1

from 1

f^-1(y) = x ------>2

2/(5-x) =y

2/y = 5-x

x = 5 - 2/y

x = (5y-2)/2

Then from 2

f^-1(y)= (5y-2)/2

Therefore, f^-1(x) = (5x - 2)/2