Question

The relation $f$ and $g$ are defined by
$f(x)= \begin{cases}x^2, & 0 \leq x \leq 3 \\ 3 x, & 3 \leq x \leq 10\end{cases}$
and $g(x)=\begin{cases}x^2, & 0 \leq x \leq 2 \\ 3 x, & 2 \leq x \leq 10\end{cases}$, then

• A. $f$ is a function
• B. $g$ is a function
• C. Both (a) and (b)
• D. None of the above

Answer 1

Answer: (A)

We have, $f(x)=\begin{cases}x^2, 0 \leq x \leq 3 \\ 3 x, 3 \leq x \leq 10\end{cases}$
Since, every element has unique image by $f$. So, $f$ is a function.
Now, $ g(x)=\begin{cases}x^2, 0 \leq x \leq 2 \\ 3 x, 2 \leq x \leq 10\end{cases}$
Since, $ g(2)=2^2=4$
and $ g(2)=3(2)=6$.
2 has two images. So, $g$ is not a function.