Convexity of $f(A)=x^TA^{-1}x$ and $f(x,A)=x^TA^{-1}x$.

Question

For $x\in\mathbb{R}^n$ and $A\in\mathbb{S_{++}^n}$ (symmetric positive definite), it is very well known that $f(x)=x^TA^{-1}x$ is convex since $A^{-1}$ is positive definite.

I wonder what if we change the function input, i.e.

1) $f(A)=x^TA^{-1}x$,

2) $f(x,A)=x^TA^{-1}x$.