Question

If f is one-to-one and f(7)=3, then f^1(3)= ___, and (f(7))^-1= ___

Answer 1

`f^(-1)(3) = \boxed{7}`

`f(f(7))^(-1) = \boxed{7}`

Explanation:

These follow from two of the properties of inverse functions:

If
`f` is a one-to-one function then

• 
  `if\; f(x) = y \;then\; f^(-1)(x) = y}`
• 
  `f^(-1)(f(x) = x\\\\f^(-1)(f(x) \;is\;the\;same\;as; ((f(x))^(-1)`