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Question Number 167336 by mnjuly1970 last updated on 13/Mar/22

          0< x<(π/2)        f(x)= ((sin(x)   ))^(1/(20))  + ((cos(x)))^(1/(20))            R_( f)  =?  (Range )

$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}<\:{x}<\frac{\pi}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{f}\left({x}\right)=\:\sqrt[{\mathrm{20}}]{{sin}\left({x}\right)\:\:\:}\:+\:\sqrt[{\mathrm{20}}]{{cos}\left({x}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:{R}_{\:{f}} \:=?\:\:\left({Range}\:\right) \\ $$$$ \\ $$

Answered by MJS_new last updated on 13/Mar/22

0<f(x)<2^(39/40)

$$\mathrm{0}<{f}\left({x}\right)<\mathrm{2}^{\mathrm{39}/\mathrm{40}} \\ $$

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