Question

If $f\left(x\right)=\{\begin{array}{ccc}-x^2,& when& x\le 0\\ 5x-4,& when& 0<x\le 1\\ 4x^2-3x,& when& 1<x<2\\ 3x+4,& when& x\ge 2\end{array}$, then

• A. f(x) is continuous at x = 0
• B. f(x) is continuous x = 2
• C. f(x) is discontinuous at x = 1
• D. None of these

Answer 1

The correct option is B f(x) is continuous x = 2

${lim}_{x\to 0-}f\left(x\right)=0$
$f\left(0\right)=0,{lim}_{x\to 0+}f\left(x\right)=-4$
f(x) discontinuous at x = 0
and ${lim}_{x\to 1-}f\left(x\right)=1$ and ${lim}_{x\to 1+}f\left(x\right)=1,f\left(1\right)=1$
Hence f(x) is continuous at x = 1.
Also ${lim}_{x\to 2-}f\left(x\right)=4(2{)}^2-3.2=10$
f(2) = 10 and ${lim}_{x\to 2+}f\left(x\right)=3\left(2\right)+4=10$
Hence f(x) is continuous at x = 2