Doubt from calculus


Q3 pls give hint...

Pls also tell how to solve the next question after 3...

See its olympaid type problem u have asked that before (imo 2001) problem type u asked for 4 degree same problem

hint - mod inequality

Question is wrong Take f(x)=1-2(x-1)^2.

May be he mean |f(x)|\leq 1.

@Jagdish_Singh sir its f'(x) only

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actually in question it is given f(|x|)\leq 1.

It may be mistake u told that in above post i thought little bit diffrent sorry sir
After that what is ur approach if its |f(x)| \le 1

Same as above....

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@Sneha_2021 could you pls explain the last step?

Mod equality used