Question

if f(x)= 4ˣ/4ˣ+2, then f(x) + f(1-x) is equal to-
(a) 0
(b) -1
(c) 1
(d) 4

Answer 1

Answer:

option: (c) 1

Explanation:

$given \: \: \: \: f(x) = \frac{ {4}^{x} }{ {4}^{x} + 2} \\ now \: \: \: f(x) + f(1 - x) \\ = \frac{ {4}^{ x} }{ {4}^{x} + 2} + \frac{ {4}^{1 - x} }{ {4}^{1 - x} + 2} \\ = \frac{ {4}^{x} }{ {4}^{x} + 2} + \frac{ \frac{4}{ {4}^{x} } }{ \frac{4}{ {4}^{x} } + 2} \\ = \frac{ {4}^{x} }{ {4}^{x} + 2} + \frac{4}{4 + 2. {4}^{x} } \\ = \frac{ {4}^{x} }{ {4}^{x} + 2} + \frac{2}{2 + {4}^{x} } \\ = \frac{ {4}^{x} + 2 }{ {4}^{x} + 2} = 1$