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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If $f (x)=\left\{\begin{array}{l}x, x \geq 0 \\ x^2, x<0\end{array}\right.$, then $f (x)$ is
  • ✓
    continuous on R
  • B
    discontinuous on R
  • C
    continuous on R except at x = 0
  • D
    discontinuous on R except at x = 0
✓

Answer

Correct option: A.
continuous on R
(A)
For $x>0, f (x)=x$
Since f is a polynomial function, it is continuous for all $x>0$.
For $x<0, f (x)=x^2$
Since f is a polynomial function, it is continuous for all $x<0$.
$\lim _{x \rightarrow 0^{-}} f (x)=\lim _{x \rightarrow 0} x^2=0$
$\lim _{x \rightarrow 0^{+}} f (x)=\lim _{x \rightarrow 0^{+}} x=0$
$f(0)=0$
$\therefore f (x)$ is continuous at $x=0$.
$\therefore f (x)$ is continuous on R .

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