# Polynomials and inverses

• March 22nd 2010, 03:44 AM
frenchguy87
Polynomials and inverses
If $h(x)=x^3 +2x+1$ has an inverse $h^{-1}$ on $\mathbb{R}$ , how would you find the value of $(h^{-1})')(y)$ at the points corresponding to $x=0,1,-1$ ?
• March 22nd 2010, 04:14 AM
tonio
Quote:

Originally Posted by frenchguy87
If $h(x)=x^3 +2x+1$ has an inverse $h^{-1}$ on $\mathbb{R}$ , how would you find the value of $(h^{-1})')(y)$ at the points corresponding to $x=0,1,-1$ ?

By a well-known theorem, $(h^{-1})'=\frac{1}{h'}$ , with the proper variables in each, so in this case $(h^{-1})'(1)=\frac{1}{h'(0)}=\frac{1}{2\cdot 0^2+2}=\frac{1}{2}$ , since $h(0)=1\Longleftrightarrow h^{-1}(1)=0$ ...now you ty to do the other ones.

Tonio