Define and . Consider the function h(x)= f(x)+g(x) f(x)g(x) . The domain of…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Define

f(x)=\dfrac{1}{x+1}

and

g(x)=\sqrt{3-x}

. Consider the function

h(x)=\frac{f(x)+g(x)}{f(x)g(x)}.

The domain of

h

is (a)

(-\infty,3)

(b)

(-\infty,-1)\cup(-1,3]

(c)

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

(d)

(-\infty,-1)\cup(-1,3)