Even Extension of a Function

Q. If $f\left(x\right)$ is an even function and satisfies the relation $x^{2}f\left(x\right)-2f\left(\frac{1}{x}\right)=g\left(x\right),$ where $g\left(x\right)$ is an odd function, then $f\left(5\right)$ equals

1. $0$
2. $\frac{50}{75}$
3. $\frac{49}{75}$
4. $-1$

Q. Which among the following graph(s) represents an odd function

1. 
2. 
3. 
4. 

Q. Which among the following function graph(s) are symmetrical about $y-$axis?

1. $f_1\left(x\right)=x\left(\frac{7^x-1}{7^x+1}\right)$
2. $f_2\left(x\right)=x^2+2$
3. $f_3\left(x\right)=\frac{1}{x},x\ne 0$
4. $f_4\left(x\right)=x^3+3$

Q. Let $f\left(x\right)=x+|x-100|-|x+100|$ and $g\left(x\right)=|f\left(x\right)|-1,$ then

1. $f\left(x\right)$ is an odd function
2. $g\left(x\right)$ is an even function
3. $f\left(x\right)$ is neither even nor odd
4. $g\left(x\right)=0$ has $6$ solutions

Q. $f\left(x\right)=\frac{a^{-x}+a^x}{2}+\cos x$ is

1. an odd function.
2. an even function.
3. neither odd nor even function.
4. both odd nor even function.

Q. If the real valued function $f\left(x\right)=\frac{a^x-1}{x^n(a^x+1)}$ is even and $n\in N$, then least possible value of $n$ is

Q. If $f:[-2,2]\to R$ defined by $f\left(x\right)=x^3+\tan x+\left[\frac{x^2+1}{p}\right]$ is an odd function, then the least value of $\left[p\right]$ is
($[.]$ represents the greatest integer function)

Q. If $f\left(x\right)$ is an even function and satisfies the relation $x^{2}f\left(x\right)-2f\left(\frac{1}{x}\right)=g\left(x\right),$ where $g\left(x\right)$ is an odd function, then $f\left(5\right)$ equals

1. $\frac{49}{75}$
2. $\frac{50}{75}$
3. $-1$
4. $0$