Show that applying a function $f(x)$ to the matrix $A$ gives $f(A) = V f(D)V^{−1}$ where $A = V DV^{−1}$. [closed]

Question

Recall that a matrix $A$ has an eigen-decomposition $A = V DV^{−1}$, where $D$ is diagonal and $V$ is the matrix of eigenvectors.

(a) Applying a function $f(x)$ to the matrix $A$ gives

$$f(A) = V f(D)V^{−1}$$

where $f(D) = \operatorname{diag}[f(\lambda_1), f(\lambda_2), \ldots]$ for eigenvalues $\lambda_1, \lambda_2, \ldots$

(i) Show that equation (1) holds for a quadratic function $f(x) = a_0 + a_1x + a_2x^2$ .