Even Function

Q. Let $f\left(x\right)=a^x(a>0)$ be written as $f\left(x\right)=f_1\left(x\right)+f_2\left(x\right)$, where $f_1\left(x\right)$ is an even function and $f_2\left(x\right)$ is an odd function. Then $f_1(x+y)+f_1(x-y)$ equals :

1. $2f_1\left(x\right)f_1\left(y\right)$
2. $2f_1(x+y)f_1(x-y)$
3. $2f_1\left(x\right)f_2\left(y\right)$
4. $2f_1(x+y)f_2(x-y)$

Q. If the real valued function $f\left(x\right)=\frac{a^x-1}{x^n(a^x+1)}$ is even, then $n$ is equal to

1. $2$
2. $\frac{2}{3}$
3. $\frac{1}{4}$
4. $3$

Q.

If f is an even function defined on the interval (-5, 5), then the real values of x, satisfying the equation $f\left(x\right)=f\left(\frac{x+1}{x+2}\right)$ are ___.

1. $\frac{3\pm \sqrt{5}}{2}$

2. $\frac{5\pm \sqrt{3}}{2}$

3. $\frac{-3\pm \sqrt{5}}{2}$

4. $\frac{-5\pm \sqrt{3}}{2}$