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

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SUMMARY

The discussion focuses on finding the inverse of the function f(x) = √(x³ + x² + x + 2) for the input a = 4. The correct approach involves solving the equation 4 = √(x³ + x² + x + 2) directly, rather than using derivatives or the chain rule. Participants clarified that the initial equation presented for finding the inverse was incorrect and emphasized the need to isolate x to determine f^-1(a).

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

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

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

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