If the graphs of and intersect at two distinct points

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

Problem

If the graphs of

f(x)=\frac{3}{x}

and

g(x)=ax+1

intersect at two distinct points, then the range of

a

is (a)

(0,\infty)

(b)

\left(-\infty,-\frac{1}{12}\right)\cup(0,\infty)

(c)

\left(-\frac{1}{12},0\right)\cup(0,\infty)

(d)

\left(-\infty,-\frac{1}{12}\right)\cup\left(-\frac{1}{12},\infty\right)