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.