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 $x=0,1,-1$ ?
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.