Four Two Four

Algebra Level 2

Let $f(x)=\dfrac{4^x}{4^x+2}$ , then the value of $f(x)+f(1-x)$ is?

x

-1

1

2x

2 solutions

Tanishq Varshney
Mar 27, 2015

$\dfrac{4^x}{4^x+2}+\dfrac{4^{1-x}}{4^{1-x}+2}$

$\dfrac{4^x}{4^x+2}+\dfrac{4}{2(4^x+2)}$

$\dfrac{4^x+2}{4^x+2}=1$

or for more ease!! put x=0!! (for those who r too lazy to solve)

A Former Brilliant Member - 6 years, 2 months ago

why 4^(1-x)/(4^(1-x)+2)=4/2(4^(x)+2)?

Septianus Antonius - 6 years, 2 months ago

Atika Samiha
Mar 28, 2015

f(1-x)=4^(1-x)/[4^(1-x)+2] =4x4^-x/[(4x4^-x) +2] =4/[4+(2x4^x)] f(x)+f(1-x)=(2+4^x)/(2+4^x) =1