April 27, 2015

Homework Help: Calculus

Posted by Kelly on Tuesday, March 31, 2009 at 5:57pm.

Let h(x)= x^3 + 4x -2. Let g(x) represent the inverse of h(x).
Find g(14).

I know that if (a, f(a)) is on h(x), then (f(a), a) will be on g(x). I also know that if f^-1(a)=b if f(b)=a. I thought that if I could find the x value(s) at which h(x)=14, I would be able to find g(14).
g(x)= x^3+4x-2=14
g(x)= x^3+4x-16=0
I don't know where to go from here. I don't know how to solve the cubic to find x.

My teacher said it was not necessary to find the equation for g(x) to solve the problem. I tried finding it at first, but ran into problems there as well:
if y= x^3+4x-2
x= y^3+4y-2
But I don't know how to solve for y.

Any help would be appreciated. Thank you.

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