Consider the piecewise defined functionf f(x) = [ . - x & if , , … - Vidyadip

MCQ

Consider the piecewise defined functionf $f(x) = \left[ \begin{gathered} \hfill \\ \hfill \\ \hfill \\ \hfill \\ \end{gathered} \right.$$\begin{gathered} \sqrt { - x} & if\,\,\,\,\,\,\,\,\,\,x < 0 \hfill \\ \hfill \\ \,\,\,\,\,\,0 & if\,\,0 \leqslant x \leqslant 4 \hfill \\ \hfill \\ x - 4 & if\,\,\,\,\,\,\,\,\,\,x > 4 \hfill \\ \end{gathered} $ choose the answer which best describes the continuity of this function

A
The function is unbounded and therefore cannot be continuous.
B
The function is right continuous at $x = 0$
C
The function has a removable discontinuity at $0$ and $4$, but is continuous on the rest of the real line.
✓
The function is continuous on the entire real line

✓

Answer

Correct option: D.

The function is continuous on the entire real line

d
Refer to the graph

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