For the function $f(x) =\left\{\begin{matrix}\frac{1-x}{|x-1|}&;x<1\\1&;x=1\\x^2&;x>1\end{matrix}\right.$ which of the following is true
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → it is continuous at all points
$f(x) =\left\{\begin{matrix}\frac{1-x}{|x-1|}&;x<1\\1&;x=1\\x^2&;x>1\end{matrix}\right.$
we know, $|x-1|=1-x$ for $x<1$
$⇒f(x) =\left\{\begin{matrix}1&;x<1\\1&;x=1\\x^2&;x>1\end{matrix}\right.$
$LHL=\lim\limits_{x→1^-}f(x)=1$
$f(1)=1$
$\lim\limits_{x→1^+}f(x)=(1)^2=1$
$LHL=RHL=f(1)$
f is continuous for every x