Question

Let $f$ be a composite function of x defined by $f\left(u\right)=\frac{1}{u^2+u-2},u\left(x\right)=\frac{1}{x-1}$.
Then the number of points x where f is discontinuous is :

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (B)

$\mu \left(x\right)=\frac{1}{x-1}$ , which is discontinous at x = 1
$f\left(u\right)=\frac{1}{u^2+u-2}=\frac{1}{\left(u+2\right)\left(u-1\right)}$,
which is discontinous at u = - 2, 1
when u = -2, then $\frac{1}{x-1}=-2\Rightarrow x=\frac{1}{2}$
when u = 1, then $\frac{1}{x-1}=1\Rightarrow x=2$
Hence given composite function is discontinous at three points, $x=1,\frac{1}{2}$ and 2.