# Thread: Finding the Inverse of a function when not given what f(x) is

1. ## Finding the Inverse of a function when not given what f(x) is

Assume that the function f is a one-to-one function

If f(6)=4, find f^−1(4).

and

The same thing but when given the inverse:

If f^−1(−2)=−5, find f(−5).

2. Originally Posted by Lolcats
Assume that the function f is a one-to-one function

If f(6)=4, find f^−1(4).

and

The same thing but when given the inverse:

If f^−1(−2)=−5, find f(−5).
Since the function is injective it has a left-inverse. Thus we have that $f(-5)=?\implies -5=f^{-1}(?)$.

3. Originally Posted by Lolcats
Assume that the function f is a one-to-one function

If f(6)=4, find f^−1(4).

and

The same thing but when given the inverse:

If f^−1(−2)=−5, find f(−5).
Use the definition of "inverse function", of course! That is, if y= f(x) , then $x= f^{-1}(y)$. If $4= f(6)$, that is, x= 6 and y= 4, $f^{-1}(y)= f^{-1}(y)= x= ?$.

Of course, if $x= f^{-1}(y)$ then y= f(x) so the other should be easy now.

4. Thank you! That makes alot of sense!