Mathematics Question on Functions

Question

If $f(x)=\frac{2^{2 x}}{2^{2 x}+2}, x \in R$ , then $f\left(\frac{1}{2023}\right)+f\left(\frac{2}{2023}\right)+\ldots+f\left(\frac{2022}{2023}\right)$ is equal to

Answer 1

Solution

The correct answer is (A) : 1011
f(x)=4x+24x
f(x)+f(1−x)=4x+24x+41−x+241−x
=4x+24x+4+2(4x)4
=4x+24x+2+4x2
=1
⇒f(x)+f(1−x)=1
Now f(20231)+f(20232)+f(20233)+……+
………+f(1−20233)+f(1−20232)+f(1−20231)
Now sum of terms equidistant from beginning and end is 1
Sum =1+1+1+……….+1(1011 times )
=1011