Question

can anyone please solve this​

Answer 1

Answer:

1

Step-by-step explanation:

Hope it helps you pls do tell if you have any other doubt

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

$\displaystyle \: f(x) = \frac{ {4}^{x} }{ {4}^{x} + 2}$

TO DETERMINE

$f(x) + f(1 - x)$

CALCULATION

$\displaystyle \: f(x) = \frac{ {4}^{x} }{ {4}^{x} + 2}$

So

$\displaystyle \: f(1 - x)$

$\displaystyle \: = \frac{ {4}^{(1 - x)} }{ {4}^{(1 - x)} + 2}$

$\displaystyle \: = \frac{ \frac{4}{ {4}^{x} } }{{ \frac{4}{ {4}^{x} } } + 2}$

$\displaystyle \: = \frac{ 4 }{4 +2 \times {4}^{x} }$

$= \displaystyle \: \frac{2 }{ {4}^{x} + 2}$

Hence

$f(x) + f(1 - x)$

$= \displaystyle \: \frac{ {4}^{x} }{ {4}^{x} + 2} + \frac{ 2}{ {4}^{x} + 2}$

$= \displaystyle \: \frac{ {4}^{x} + 2 }{ {4}^{x} + 2}$

$= 1$