Arrey, this is a favourite with paper-setters! Just remember, for one-one, use the derivative: if f'(x) > 0 or f'(x) < 0 for all x in the domain, it's strictly monotonic and hence one-one. For onto, find range and show it equals the codomain. Mostly, they ask for functions like f(x) = 9x + 3, so it's straightforward.
Actually, my tuition student, Srivalli, got this exact question wrong in her pre-boards. While checking her paper, I realised she always forgot to explicitly state the "for all x" condition for the derivative test. Now I make her write it three times! Her improvement in the unit test, ayyo, it made my whole week.
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