Verified answer

g(x) is defined precisely when f(-x) is defined. If it helps, let y = -x. Then we need f(y) to be defined, so we need y to be in the domain of f. So y must satisfy -1 ≤ y ≤ 5.

But y = -x, so we have

-1 ≤ -x ≤ 5

Multiply through by -1 (remembering that multiplying by a negative number reverses the inequalities) we get

1 ≥ x ≥ -5

i.e. -5 ≤ x ≤ 1.

So the domain of g is {x: -5 ≤ x ≤ 1}.