Continuity proof

[warped surge]

Any help would be appreciated

[halcyon crescent]

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[broken lion]

Think about a counterexample

[warped surge]

The statement is false?

[broken lion]

I think it’s true, I meant to try come up with a counterexample to get a better idea of why it’s true

There’s also a theorem regarding bounded function over closed intervals, not sure if you have covered that yet

[compact horizon]

it is continuous in closed interval, hence there is a minimum

and by assumption f > 1 on [a,b]

so the minimum is also > 1

[warped surge]

Thanks both! I've managed to solve it @compact horizon @broken lion