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A function f(x) is defined by f(x)=\left\{\begin{array}{cc} \frac{\left[x^2\right]-1}{x^2-1}, & \text { for } x^2 \neq 1 \\ 0, & \text { for } x^2=1 \end{array}\right.  \text { Where [.]denotes G.IF }

Option: 1

 Continuous at x=-1


Option: 2

Discontinuous at x=1


Option: 3

Differentiable at x=1


Option: 4

None of these


Answers (1)

best_answer

f(x)=\left\{\begin{array}{cc} \frac{\left[x^2\right]-1}{x^2-1}, & \text { for } x^2 \neq 1 \\ 0, & \text { for } x^2=1 \end{array}\right.

=\left\{\begin{array}{ccc} \frac{-1}{x^2-1} & , \text { for } & 0<x^2<1 \\ 0 & , \text { for } & x^2=1 \\ 0 & , \text { for } & 1<x^2<2 \end{array}\right.

RHL at \mathrm{x}=1 \text { is } 0

Also LHL \text { at } x=1 \text { is } \infty

Posted by

Pankaj Sanodiya

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