Question

Let $f\left(x\right)=\frac{4^x}{4^x+2}.$ $Thenf\left(x\right)+f(1-x)$ is :

• A. 0
• B. 1
• C. -1
• D. None of these

Answer 1

The correct option is B 1

$f\left(x\right)=\frac{4^x}{4^x+2},$
$f(1-x)=\frac{4^{1-x}}{4^{1-x}+2}=\frac{4\cdot 4^{-x}}{4\cdot 4^{-x}+2}$
$=\frac{4\cdot 4^{-x}}{(4+2\cdot 4^x)\cdot 4^{-x}}=\frac{4^x+2}{2+4^x}=1$
$\therefore f\left(x\right)+f(1-x)=\frac{4^x+2}{2+4^x}=1$