Question

If you were given the function f(x) and its inverse function,


`{f}^( - 1)(x)`
, what would you expect the values of

`{f}^( - 1)(f(3))`
to be, assuming that 3 is part of the domain of f(x)? Explain your answer.​

Answer 1

3

Explanation:

if we combine a function f(x) and its inverse f-¹(x), the result will be x

f-¹(f(x)) = f(f-¹(x)) = x

you can try for any function, i.e.

f(x) = 2x + 1

f-¹(x) = (x-1)/2

f-¹(f(x)) = (2x + 1 - 1)/2 = x

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