Is concave quadratic + linear a concave function?

Question

Basic question about convexity/concavity:

Is the difference of a concave quadratic function of a matrix $X$ given by f(X) and a linear function l(X), a concave function?

i.e, is f(X)-l(X) concave?

If so/not what are the required conditions to be checked for?

Answer 1

A linear function is both concave and convex (here $-l$ is concave), and the sum of two concave functions is concave.