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Functions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSFunctions3 Marks
Question
If $\text{f(x)}=\begin{cases}\text{x}^2,&\text{when }\text{ x}<0\\\text{x},&\text{when }\ 0\leq\text{x}<1\\\frac{1}{\text{x}},&\text{when }\text{ x}>0\end{cases}$ Find:
  1. $\text{f}\Big(\frac{1}{2}\Big)$
  2. $\text{f}(-2)$
  3. $\text{f}(1)$
  4. $\text{f}(\sqrt{3})$
  5. $\text{f}(\sqrt{-3})$
✓

Answer

We have, $\text{f(x)}=\begin{cases}\text{x}^2,&\text{when }\text{ x}<0\\\text{x},&\text{when }\ 0\leq\text{x}<1\\\frac{1}{\text{x}},&\text{when }\text{ x}>0\end{cases}$
  1. $\text{f}\Big(\frac{1}{2}\Big)=\frac{1}{2}$
  2. $\text{f}(-2)=(-2)^2=4$
  3. $\text{f}(1)=\frac{1}{1}=1$
  4. $\text{f}(\sqrt{3})=\frac{1}{\sqrt{3}}$
  5. $\text{f}(\sqrt{-3})=$ does not exist because $\sqrt{3}\notin$ domain (f).

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