The function given by fx - 1-x- -1-x22 is continuous in

1|x| 1 is discontinuous where |x|=1 i.e., x= 1,1 while x^22 is continuous for all real x. So, f(x )=1|x| 1 x^22 is discontinuous at x= 1,1 Hence, f(x) is con ...

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Standard XII

Mathematics

One-One into Function

The function ...

Question

The function given by $f (x) = \frac{1}{| x | - 1} - \frac{x^{2}}{2}$ is continuous in

R - {- 1, 1}

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R - {1}

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R - {- 1}

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{- 1, 1}

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Solution

The correct option is A $R - {- 1, 1}$
$\frac{1}{| x | - 1}$ is discontinuous where $| x | = 1$
i.e., $x = - 1, 1$
while $\frac{x^{2}}{2}$ is continuous for all real $x .$
So, $f (x) = \frac{1}{| x | - 1} - \frac{x^{2}}{2}$ is discontinuous at $x = - 1, 1$
Hence, $f (x)$ is continuous for all $x \in R - {- 1, 1}$

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The function given by f(x)=1|x|−1−x22 is continuous in

The correct option is A R−{−1,1}1|x|−1 is discontinuous where |x|=1 i.e., x=−1,1 while x22 is continuous for all real x. So, f(x)=1|x|−1−x22 is discontinuous at x=−1,1 Hence, f(x) is continuous for all x∈R−{−1,1} ​​

The function given by $f (x) = \frac{1}{| x | - 1} - \frac{x^{2}}{2}$ is continuous in