Question

The function $ f(x)=\frac{2{{x}^{2}}+7}{{{x}^{3}}+3{{x}^{2}}-x-3} $ is discontinuous for

• A. $ x=1 $ only
• B. $ x=1 $ and $ x=-1 $ only
• C. $ x=1,\,x=-1,\,x=-3 $ only
• D. $ x=1,\,x=-1,\,x=-3 $ and other values of x

Answer 1

Answer: (C)

Given, $ f(x)=\frac{2{{x}^{2}}+7}{{{x}^{3}}+3{{x}^{2}}-x-3} $
$ =\frac{2{{x}^{2}}+7}{({{x}^{2}}-1)(x+3)} $
At $ x=1,\,\,f(x)=\infty $
$ x=-1,\,f(x)=\infty $
$ x=-3,\,f(x)=\infty $
$ \therefore $ At $ x=1,\,\,\,x=-1 $
and $ x=-3 $ function is discontinuous