For the function fx use composition of functions to show tha

For the function f(x), use composition of functions to show that f^-1 (x) is as given. f(x) = 2/5 x + 1, f^-1 (x) = 5x - 5/2

Solution

f(x) = 2x/5 +1

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

Use composistion of function : f(f^-1(x)): plug x = f^-1(x) in f(x)

f(f^-1(x)) = (2/5)(5x-5)/2 +1

= (5x-5)/5 +1

= x -1 +1

= x

This shows that f^-1(x) is inverse of f(x)