Question

$f:[0,\infty )\to B$ defined by $f\left(x\right)=x^2-4$ is a function. If $B=[k,\infty )$, then the maximum value possible for $k$ is

Answer 1

$f\left(x\right)=x^2-4$
For $0\le x<\infty$,
$0\le x^2<\infty$
$\therefore -4\le x^2-4<\infty$
$\therefore R\left(f\right)=[-4,\infty )$
So, $k$ can be any real number satisfying $k\le -4$
So the maximum value of $k$ is $-4$