Answer
$||g||=\frac{1}{\sqrt{105}}$
Work Step by Step
For f and g in C[0,1], the inner product is defined as follows
$\langle g,g\rangle=\int_0^1g(t)g(t)dt=\int_0^1(t^3-t^2)(t^3-t^2)dt=\int_0^1(t^6-2t^5+t^4)dt=\left[\frac{t^7}{7}-\frac{t^6}{3}+\frac{t^5}{5}\right]_0^1=\frac{1}{105}$
$||g||=\frac{1}{\sqrt{105}}$
