Even and Odd Functions

Among of the following functions  find an even function?

Let $f:[-2, 2]\to R$ be an odd function defined as $f\left(x\right)=x^3+\tan x+\left[\frac{x^2+1}{\lambda }\right],$ then $\lambda$ belongs to

(where $\left[·\right]$ denotes the greatest integer function)

The function $f\left(x\right)=\left|x\right|-x^3$ is

If $f\left(x\right)=2017\tan \left|x\right|+3x^3\sin x+x^{2018}-3x^2+2x^3$ and $f\left(3\right)=116,$ then $f\left(–3\right)$ is equal to

Let $f$ be an odd function defined on the real number such that $f\left(x\right)=3\sin x+4\cos x$$,$ for $x\ge 0$$,$ then $f\left(x\right)$ for $x<0$ is

$\underset{-1}{\overset{1}{\int }}\frac{\sqrt{1+x+x^2}-\sqrt{1-x+x^2}}{\sqrt{1+x+x^2}+\sqrt{1-x+x^2}}dx=$

If $\mathrm{f}$ is a real valued function defined by $\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)+\mathrm{f}\left(\mathrm{x}-\mathrm{y}\right)=\mathrm{f}\left(2\mathrm{x}\right)$ , then the value of $\underset{\mathrm{f}\left(2\right)}{\overset{\mathrm{f}\left(-2\right)}{\int }}\mathrm{f}\left(\mathrm{x}\right)$ is equal to

If $f\left(x\right)$ is an even function and $f^{\text{'}}\left(x\right)$ exist for all 'x' then $f^{\text{'}}\left(1\right) + f^{\text{'}}(–1)$ is-

Let $f\left(x\right)=\frac{\mathrm{s}\mathrm{i}{\mathrm{n}}^{101}x}{\left[\frac{x}{\pi }\right]+\frac{1}{2}}$ , where $\left[x\right]$ denotes the integral part of $x$ is

If $f\left(x\right)$ is an even function defined on $\left(-5,\mathrm{ }\mathrm{ }5\right)$, then a value of $x$ satisfying the equation $f\left(x\right)=f\left(\frac{x+1}{x+2}\right)$ is

Let $f\left(x\right)=\frac{\mathrm{s}\mathrm{i}{\mathrm{n}}^{101}x}{\left[\frac{x}{\pi }\right]+\frac{1}{2}}$ , where $\left[x\right]$ denotes the integral part of $x,$ then $f\left(x\right)$ is

If $\mathrm{f}\left(\mathrm{x}\right)=4{\mathrm{x}}^8$ , then

Let $f\left(-x\right)=f\left(x\right)$. Then $f^{\text{'}}\left(x\right)$ must be

If $f:R\to R$ is an even function having derivatives of all orders, then an odd function among the following is

If $f\left(x\right)$ is an odd periodic function with period 2, then $f\left(4\right)$ equals

The function $f\left(x\right)=\log (x+\sqrt{x^2+1})$ is

If $f\left(x\right)=2x^6+3x^4+4x^2$, then $f^{\text{'}}\left(x\right)$ is

$f: R\to R;$ $f\left(x\right)=\left(\frac{e^{2x}-1}{e^{2x}+1}\right)$ is

If $f\left(x\right)$ is an even function and $f^{\prime }\left(x\right)$ exists, then $f^{\prime }\left(e\right)+f^{\prime }\left(-e\right)$ is

The function $f\left(x\right)$ which satisfies $f\left(x\right)=f\left(-x\right)=\frac{f^{\text{'}}\left(x\right)}{x}$, is given by