SOLUTION: Hello, Is it possible to find function f(x) such that its inverse f-1 = 1/f ? if so, what function(s) satisfies this claim? Thank you, Muneef Halawa

Algebra ->  Inverses -> SOLUTION: Hello, Is it possible to find function f(x) such that its inverse f-1 = 1/f ? if so, what function(s) satisfies this claim? Thank you, Muneef Halawa      Log On


   

Question 956968: Hello,
Is it possible to find function f(x) such that its inverse f-1 = 1/f ? if so, what function(s) satisfies this claim?

Thank you,
Muneef Halawa
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Yes,
f%28x%29=1%2Fx} has an inverse of
f%5E%28-1%29%28x%29=1%2Fx so
f%5E%28-1%29%28f%28x%29%29=1%2Ff=1%2F%281%2Fx%29=x
So the inverse is the reciprocal of the function.
Example:
f%282%29=0.5
f%5E%28-1%29%280.5%29=2
f%5E%28-1%29%28f%282%29%29=f%5E%28-1%29%280.5%29=2
So f%5E%28-1%29%28f%28x%29%29=x by definition, an inverse.