Originally Posted by

**x3bnm** I've a math problem that I can't solve which is:

How do I prove that if a function is bijective then it's inverse is also bijective?

I know I've to prove that if $\displaystyle f^{-1}(a) = f^{-1}(b)$ then $\displaystyle a = b$ So then the inverse is injective.

Then to prove a function $\displaystyle f^{-1} : B \to A$ is surjective I've to show that each element of $\displaystyle A$ is the image of at least one element of $\displaystyle B$

If I can show these two to be valid then the inverse is bijective.

Can anyone kindly tell me how do I show this?

How do I show that a inverse of a bijective function is injective and surjective?