Let a_1 , a_2 , a_3 , ...a_(2022) be numbers ranging from (0, +∞) \ {1}, for which the function f : R→R is defined as f(x)=a_1 ^x +a_2 ^x +a_3 ^x +...a_(2022) ^x . If f(2022)=f(−2022)=2022 prove that this function is constant.


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Question Number 181196 by depressiveshrek last updated on 22/Nov/22
$Let a_1 , a_2 , a_3 , ...a_(2022) be numbers ranging from (0, +∞) \ {1}, for which the function f : R→R is defined as f(x)=a_1 ^x +a_2 ^x +a_3 ^x +...a_(2022) ^x . If f(2022)=f(−2022)=2022 prove that this function is constant.$
$L e t a_{1}, a_{2}, a_{3}, . . . a_{2022} b e n u m b e r s$ $r a n g i n g f r o m (0, + \infty) ∖ {1}, f o r w h i c h$ $t h e f u n c t i o n f : R \to R i s d e f i n e d a s$ $f (x) = a_{1}^{x} + a_{2}^{x} + a_{3}^{x} + . . . a_{2022}^{x} .$ $I f f (2022) = f (- 2022) = 2022 p r o v e$ $t h a t t h i s f u n c t i o n i s c o n s t a n t .$
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