How to prove the following norms equal?

Question

Let $p_k$ be degree $k$ polynomial and $p_k = 1-\lambda q_{k-1}$ where $q_{k-1}$ is a $k-1$ degree polynomial. $C[a,b]$ be set of continuous functions equipped with sup norm. Then for $w(\lambda) = \lambda$, how to prove that $$\|p_k\|_{C[a,b]} = \left\|w\left(\frac{1}{\lambda}- q_{k-1}\right)\right\|_{C[a,b]} $$ where $w>0$ is a weight function? I have no idea how to prove this.