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  • Let be the function defined by <img alt="\mathrm{f(x)=\left\{\begin{array}{cc} \frac{x^2-1}{x^2-2|x-1

Let \mathrm{f} be the function defined by \mathrm{f(x)=\left\{\begin{array}{cc} \frac{x^2-1}{x^2-2|x-1|-1} & ; \quad x \neq 1 \\ 1 / 2 & ; \quad x=1 \end{array}\right. }

Option: 1

the function is continuous for all values of x


Option: 2

the function is continuous only for x>1


Option: 3

the function is continuous at x=1


Option: 4

the function is not continuous at x=1


Answers (1)

best_answer

For \mathrm{x<1, f(x)=\frac{x^2-1}{x^2+2 x-3}=\frac{x+1}{x+3} ; \quad \therefore \quad \lim _{x \rightarrow 1^{-}} f(x)=\frac{1}{2}}

\mathrm{For \: x>1, f(x)=\frac{x^2-1}{x^2-2 x+1}=\frac{x+1}{x-1}}

\mathrm{\therefore \quad \lim _{x \rightarrow 1^{+}} f(x)=\infty}
\mathrm{\therefore \quad} The function is not continuous at \mathrm{x= 1}

Posted by

Ajit Kumar Dubey

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