If [math] f(x) = x^3 + x + 2[/math] and [math]f(a) = 9[/math] then:

 

Calculate [math]f^{-1}(-5)[/math] 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?

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 [math]f(x) = x^2 +1[/math]

 

Set [math]y = x^2 +1 [/math]

 

Then solve for x in terms of y:

 

[math]y -1 = x^2 [/math]

 

[math]\sqrt{y - 1} = x [/math]

 

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

 

[math]x = f^{-1}(y) = \sqrt{y-1}[/math]