Let f be the function defined by f(x)=\ array ll x^ 2 -1 x^ 2 -2|x-1|-1 , & x ≠ 1 1 / 2, & x=1 array .

Correct answer: D. The function is not continuous at x=1 For x 1, f(x)= x^ 2 -1 x^ 2 -2 x+1 =(x+1)/(x-1) _ x arrow 1^ + f(x)=∞ The function is not continuous at x=1 .

BITSAT 2020

Exam: BITSAT
Year: 2020
Subject: Mathematics
Chapter: Continuity and Differentiability

BITSAT 2020 · Mathematics · Continuity and Differentiability

Let f be the function defined by f(x)=\ array ll x^ 2 -1 x^ 2...

Let

\mathrm{f}

be the function defined by

f(x)=\left\{

\begin{array}{ll}\frac{x^{2}-1}{x^{2}-2|x-1|-1}, & x \neq 1 \\ 1 / 2, & x=1\end{array}

\right.

Options

AThe function is continuous for all values of x
BThe function is continuous only for $x > 1$
CThe function is continuous at $\mathrm{x}=1$
DThe function is not continuous at $x=1$

Correct answer

D. The function is not continuous at $x=1$

Step-by-step solution

For

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

For

x > 1, f(x)=\frac{x^{2}-1}{x^{2}-2 x+1}=\frac{x+1}{x-1}\therefore \lim _{x \rightarrow 1^{+}} f(x)=\infty\therefore

The function is not continuous at

\mathrm{x}=1

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