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

Question Number 181196 by depressiveshrek last updated on 22/Nov/22

L e t a_{1}, a_{2}, a_{3}, \dots 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} + \dots 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 .