Y-1-t2-t-2 where t-1-x-1 then the number of points of discontinuities of y-fx-x - R is

T=1/x 1 is discontinuous at x=1 y=1/t^2+t 2 is discontinuous when t^2+t 2=0 Or (t+2)(t 1)=0 Or t= 2 t=1 x=1/t+1 When t= 2 y= 1/2+1=1/2 When t=1 x=1+1=2 Hence fu ...

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Standard XII

Mathematics

Points of Discontinuity

y=1/t2+t-2 wh...

Question

$y = \frac{1}{t^{2} + t - 2}$ where $t = \frac{1}{x - 1}$ then the number of points of discontinuities of $y = f (x), x ϵ R$ is

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Solution

The correct option is C 3
$t = \frac{1}{x - 1}$ is discontinuous at x=1
$y = \frac{1}{t^{2} + t - 2}$ is discontinuous when
$t^{2} + t - 2 = 0$
Or $(t + 2) (t - 1) = 0$
Or $t = - 2 t = 1$
$x = \frac{1}{t} + 1$
When $t = - 2$
$y = \frac{- 1}{2} + 1 = \frac{1}{2}$
When $t = 1$
$x = 1 + 1 = 2$
Hence function is discontinuous at 3 points

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y=1t2+t−2 where t=1x−1 then the number of points of discontinuities of y=f(x),xϵR is

The correct option is C 3t=1x−1 is discontinuous at x=1 y=1t2+t−2 is discontinuous when t2+t−2=0 Or (t+2)(t−1)=0 Or t=−2t=1 x=1t+1 When t=−2 y=−12+1=12 When t=1 x=1+1=2 Hence function is discontinuous at 3 points

$y = \frac{1}{t^{2} + t - 2}$ where $t = \frac{1}{x - 1}$ then the number of points of discontinuities of $y = f (x), x ϵ R$ is