# F(x)=4^x/4^x+2,then f(x)+f(1-x) is equal toA)0 b)-1 c)1 d)4

Saurabh Koranglekar
3 years ago
Akshat Agrawal
24 Points
3 years ago
Let the Equation (1) be -      ​$f(x) + f(1-x) = \frac{4^{x}}{4^{x} + 2} + \frac{4^{1-x}}{4^{1-x} + 2} = \frac{4^{x}(4^{1-x} + 2) + 4^{1-x}(4^{x} + 2)}{(4^{x} + 2)(4^{1-x} + 2)}$

Now we can write ,   $4^{1-x}(4^{x} + 2) = 4 + 2*4^{1-x} = 2(2 + 4^{1-x}) = 2(4^{1-x} + 2)$    (all i did is to multiply the numbers and rearrange them in a specific order).Let this be equation (2)

So we have equation (1) (using equation (2)) as -
$f(x) + f(1-x) = \frac{4^{x}(4^{1-x} + 2) + 4^{1-x}(4^{x} + 2)}{(4^{x} + 2)(4^{1-x} + 2)} = \frac{4^{x}(4^{1-x} + 2) + 2(4^{1-x} + 2)}{(4^{x} + 2)(4^{1-x} + 2)} \\\\ = \frac{(4^{1-x} + 2)(4^{x} + 2)}{(4^{x} + 2)(4^{1-x} + 2)} = 1$

This gives us the answer as 1. So the answer is option (c)