Given and , find the domain of…

MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions

Problem

Given

f(x)=\sqrt{5-x}

and

g(x)=\dfrac{1}{x-2}

, find the domain of

(f+g)(x)

. (a)

(2,5]

(b)

(-\infty,2)\cup(2,5]

(c)

(-\infty,5]

(d)

(-\infty,2)\cup(2,\infty)