A Question 'bout Functions

[mehran]

If $f(x) = x^3 + x + 2$ and $f(a) = 9$ then:

 

Calculate $f^{-1}(-5)$ at "a".

This is the question that i'm thinking of it but i can't solve it at all!

Does anyone know that how i can get to the answer?

[Bignose]

Given a f(x), you can find the inverse (if one exists, there certainly doesn't HAVE to be an inverse) by setting y=f(x) and then solving just for x.

 

For example: let $f(x) = x^2 +1$

 

Set $y = x^2 +1$

 

Then solve for x in terms of y:

 

$y -1 = x^2$

 

$\sqrt{y - 1} = x$

 

Then once you've isolated x, this is the inverse function:

 

$x = f^{-1}(y) = \sqrt{y-1}$