Let f be a composite function of x defined by f(u)=frac1u^2+u-2 , u(x)=(1)/(x-1) . Then the number of points x where f is discontinuous is :

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JEE Main 2013 (Online) 23rd AprilQuestion 1

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

Functions

$4$$3$✓ Correct answer$2$$1$

Solution

$u^2+u-2=(u+2)(u-1)=0$ gives $u=1,-2$, i.e. $x=2,\frac12$; also $u$ is undefined at $x=1$. So $3$ points.

Functions - JEE Mathematics question (JEE Main 2013 (Online) 23rd April)

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