Chapter 3.3, Problem 69ES

Let $f\left(x\right)=x^4+x^3+1,0\le x\le 2$ .

(a) Show that $f$ is one-to-one.

(b) Let $g\left(x\right)=f^{-1}\left(x\right)$ and define $F\left(x\right)=f\left(2g\left(x\right)\right)$ . Find an equation for the tangent line to $y=F\left(x\right)$ at $x=3$ .