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).

Quote:

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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).

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Since the function is injective it has a left-inverse. Thus we have that .

Quote:

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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).

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Use the definition of "inverse function", of course! That is, if y= f(x) , then . If , that is, x= 6 and y= 4, .

Of course, if then y= f(x) so the other should be easy now.

Thank you! That makes alot of sense!