Question

The relation f is defined by f(x) = $\{\begin{array}{cc}{x}^2,& 0\le x\le 3\\ 3x,& 3\le x\le 10\end{array}$ and

The relation g is defined by g(x) = $\{\begin{array}{cc}{x}^2,& 0\le x\le 2\\ 3x,& 2\le x\le 10\end{array}$ Then,

• A. 'f' is a function and 'g' is not a function
• B. 'g' is a function and 'f' is not a function
• C. Both 'f' and 'g' are functions
• D. neither 'f' nor 'g' are functions

Answer 1

The correct option is A 'f' is a function and 'g' is not a function

Both f and g have multiple definitions at x=3 and x=2 respectively.
$f\left(3\right)=3^2=9(\because f(x)=x^2)$
Also, $f\left(3\right)=3\times 3=9(\because f(x)=3x)$
f(3) is unique.
$g\left(2\right)=2^2=4(\because g(x)=x^2)$
Also, $g\left(2\right)=3\times 2=6(\because g(x)=3x)$
g(2) is not unique
Hence 'f' is a function but 'g' is not