Is this function bounded or not?

Question

$f(x) = \left(1-\frac ax\right)^2$

where both $x>0$, $a>0$

Is this function bounded? i.e. is there an M such that $f(x) ≤ M < \infty$ ?

How can I figure this out?

Thanks very much in advance and apologies for notation, I am newbie.

Answer 1

No. Let $a > 0$. Then, since $f(x) = (1-\frac{a}{x})^{2} \to \infty$ as $x \to 0+$, the function $f$ is unbounded on $]0, \infty[$.