Question Number 181196 by depressiveshrek last updated on 22/Nov/22
$${Let}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:...{a}_{\mathrm{2022}} \:{be}\:{numbers} \\ $$$${ranging}\:{from}\:\left(\mathrm{0},\:+\infty\right)\:\backslash\:\left\{\mathrm{1}\right\},\:{for}\:{which} \\ $$$${the}\:{function}\:{f}\::\:\mathbb{R}\rightarrow\mathbb{R}\:{is}\:{defined}\:{as} \\ $$$${f}\left({x}\right)={a}_{\mathrm{1}} ^{{x}} +{a}_{\mathrm{2}} ^{{x}} +{a}_{\mathrm{3}} ^{{x}} +...{a}_{\mathrm{2022}} ^{{x}} . \\ $$$${If}\:{f}\left(\mathrm{2022}\right)={f}\left(−\mathrm{2022}\right)=\mathrm{2022}\:{prove} \\ $$$${that}\:{this}\:{function}\:{is}\:{constant}. \\ $$