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Question Number 31865 by rahul 19 last updated on 16/Mar/18

$$Rangeoffunction:$$$$f\left(x\right)=6^x+3^x+6^{-x}+3^{-x}+2.$$

Commented by rahul 19 last updated on 16/Mar/18

$$mytry:$$$$f\left(x\right)={(6^{\frac{x}{2}}+6^{\frac{-x}{2}})}^2+{(3^{\frac{x}{2}}+3^{\frac{-x}{2}})}^2-2⩾6.$$$$hencerangeis[-6,\mathrm{\infty }).$$

Commented by rahul 19 last updated on 16/Mar/18

$$butans.givenis[6,\mathrm{\infty }).$$

Commented by Tinkutara last updated on 16/Mar/18

Apply AM-GM.

Commented by rahul 19 last updated on 16/Mar/18

$$plztellwhereamiwrong?$$

Commented by Tinkutara last updated on 16/Mar/18

$$Becauseyouassumedminimum$$$$valueof{6}^{\frac{x}{2}}+6^{\frac{-x}{2}}tobe0whichisnot.$$$$6^{\frac{x}{2}}+6^{\frac{-x}{2}}hasminimumvalue2.$$

Commented by rahul 19 last updated on 16/Mar/18

$$okthanks!!$$

Answered by mrW2 last updated on 16/Mar/18

$$f\left(x\right)=(6^x+6^{-x})+(3^x+3^{-x})+2$$$$⩾2+2+2=6$$

Commented by rahul 19 last updated on 16/Mar/18

$$yessir,ihavegottheans.$$$$thankusir!$$

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