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Find the points of discontinuity of $y=\large\frac{1}{u^2+u-2}$ where $u=\large\frac{1}{x-1}$

$(a)\;1,-1\qquad(b)\;\large\frac{1}{2}$$,0\qquad(c)\;0,1\qquad(d)\;\large\frac{1}{2}$$,1,2$

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$u=f(x)=\large\frac{1}{x-1}$ is discontinuous at x=1
The function $y=g(x)=\large\frac{1}{u^2+u-2}$
$\Rightarrow \large\frac{1}{(u+2)(u+1)}$ is discontinuous at $u=-2,1$
When $u=-2,x=\large\frac{1}{2}$ and when $u=1,x=2$
$\therefore$ The composite function $y=g(f(x))$ is discontinuous at three points $x=\large\frac{1}{2}$$,1,2$
Hence (d) is the correct answer.
answered Dec 31, 2013 by sreemathi.v
 

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