Answer
$\langle f,f\rangle=\frac{2}{\sqrt{5}}$
Work Step by Step
For f and g in C[0,1], the inner product is defined as follows
$\langle f,f\rangle^2=\int_0^1f(t)f(t)dt=\int_0^1(1-3t^2)(1-3t^2)dt=\int_0^1(1-6t^2+9t^4)dt=\left[t-2t^3+\frac{9t^5}{5}\right]_0^1=\frac{4}{5}$
$\langle f,f\rangle=\frac{2}{\sqrt{5}}$
