Sum of convex and decreasing function

Question

I have a sum of decreasing function and a convex function over some domain. Can I say that the sum is also a convex function (i.e. there exists a unique minimum)?

Answer 1

$f(x)=x^2$ is convex and $g(x)=\sqrt{x}-x^2$ is decreasing on $[1,\infty)$, but $f(x)+g(x)=\sqrt{x}$, which is concave.