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

• Jan 20th 2010, 12:36 PM
Lolcats
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).
• Jan 20th 2010, 12:48 PM
Drexel28
Quote:

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 \$\displaystyle f(-5)=?\implies -5=f^{-1}(?)\$.
• Jan 20th 2010, 12:51 PM
HallsofIvy
Quote:

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 \$\displaystyle x= f^{-1}(y)\$. If \$\displaystyle 4= f(6)\$, that is, x= 6 and y= 4, \$\displaystyle f^{-1}(y)= f^{-1}(y)= x= ?\$.

Of course, if \$\displaystyle x= f^{-1}(y)\$ then y= f(x) so the other should be easy now.
• Jan 20th 2010, 06:47 PM
Lolcats
Thank you! That makes alot of sense!