Question

The relation $f$ and $g$ are defined by
$f(x)=\{\begin{array}{ll}{x}^2,& 0\le x\le 3\\ 3x,& 3\le x\le 10\end{array}$
and $g(x)=\{\begin{array}{ll}{x}^2,& 0\le x\le 2\\ 3x,& 2\le x\le 10\end{array}$, 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, $f(x)=\{\begin{array}{l}{x}^2,0\le x\le 3\\ 3x,3\le x\le 10\end{array}$
Since, every element has unique image by $f$. So, $f$ is a function.
Now, $g(x)=\{\begin{array}{l}{x}^2,0\le x\le 2\\ 3x,2\le x\le 10\end{array}$
Since, $g(2)=2^2=4$
and $g(2)=3(2)=6$.
2 has two images. So, $g$ is not a function.