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Functions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSFunctions3 Marks
Question
The function f is defined by $\text{f(x)}=\begin{cases}\text{x}^2,& 0\leq\text{x}\leq3\\3\text{x},&3\leq\text{x}\leq10\end{cases}$ The relation g is defined by $\text{g(x)}=\begin{cases}\text{x}^2,& 0\leq\text{x}\leq2\\3\text{x},&2\leq\text{x}\leq10\end{cases}$ Show that f is a function and g is not a function.
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Answer

We have, $\text{f(x)}=\begin{cases}\text{x}^2,& 0\leq\text{x}\leq3\\3\text{x},&3\leq\text{x}\leq10\end{cases}$ and $\text{g(x)}=\begin{cases}\text{x}^2,& 0\leq\text{x}\leq2\\3\text{x},&2\leq\text{x}\leq10\end{cases}$ Now, $f(3) = (3)^2 = 9$ and $f(3) = 3 × 3 = 9$ and $g(2) = (2)^2 = 4$ and $g(2) = 3 × 2 = 6$ We observe f(x) takes unique value at each point in its domain$ [0, 10]$. However g(x) does not takes unique value at each in its domain $[0, 10]$ Hence, g(x) is not a function.

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