Let and . Find the domain of the product…

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

Problem

Let

f(x)=\sqrt{6-x}

and

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

. Find the domain of the product

(f\,g)(x)

. (a)

(-\infty,6]

(b)

(1,6]

(c)

(-\infty,1)\cup(1,6]

(d)

(-\infty,1)\cup(1,6)