How do I find the inverse of a function with a given input?

[10min]

Homework Statement

Find (f^-1) (a) if f(x) = sqrt of (x^3+x^2+x+2) and a = 4?

Homework Equations

Find (f ^-1) (a) = 1/ f ^1( f ^-1(a))

The Attempt at a Solution

Take Derivative
1/2(x^3+x^2+x+2)^-(1/2)
do I need to do chain rule?
I am lost
this problem can help me pass the class
please help

 

[Mark44]

This problem has nothing to do with derivatives or the chain rule or reciprocals.
$$x = f^{-1}(a) \iff a = f(x)$$

So basically, what you need to do is solve the equation $$4 = \sqrt{x^3 + x^2 + x + 2}$$

BTW, this doesn't make any sense at all: (f ^-1) (a) = 1/ f ^1( f ^-1(a))