If-f-x-4-x-4-x-2-find-f-1-17-f-16-17-

Question Number 150469 by mathdanisur last updated on 12/Aug/21

If f (x) = \frac{4^{x}}{4^{x} + 2} find f (\frac{1}{17}) + f (\frac{16}{17}) \overset{?}{=}

Answered by gsk2684 last updated on 12/Aug/21

f (x) + f (1 - x) = \frac{4^{x}}{4^{x} + 2} + \frac{4^{1 - z}}{4^{1 - x} + 2}

= \frac{4^{x}}{4^{x} + 2} + \frac{4}{4 + 2 . 4^{x}} = \frac{4^{x}}{4^{x} + 2} + \frac{2}{2 + 4^{x}} = 1

f (x) + f (1 - x) = 1 \Rightarrow f (\frac{1}{17}) + f (\frac{16}{17}) = 1

Commented by mathdanisur last updated on 12/Aug/21

Thank You Ser