Even and Odd Functions

Check whether the function $f\left(x\right)=\frac{{\left(1+2^x\right)}^7}{2^x}$ is

The function $f\left(x\right)=\frac{x}{e^x-1}+\frac{x}{2}+1$ is

Determine whether the following is even or odd.

$f\left(x\right) = \sin x.\cos x$

Determine whether the following is even or odd.

$f\left(x\right)=x^2-\left|x\right|$

Which one of the following has point symmetry about the origin?

Which one of the following letters has point symmetry?

If $f\left(x\right)=x^3+x$, which of the following statements must be true?

Draw the odd function graph for $f\left(x\right)=x^3+2x$ and state why is it an odd function.

Prove that the function $f\left(x\right)=x^{2n}$, where $n$ is an integer is an even function

Identify the even function from the given functions.

$f\left(x\right)=\sin x$ is an odd function.

$f\left(x\right)=x^2$ is an even function.

The graph of an even function is symmetric about $y$-axis.

$f\left(x\right)=\cos x$ is an even function.

Determine whether the following is even or odd.

$f\left(x\right)=\log \left(\frac{1-x}{1+x}\right)$

Determine whether the following is even or odd.

$f\left(x\right)=x\left(\frac{a^x+1}{a^x-1}\right)$

Which of the following is false?

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

If $f:R\to R$ be a function satisfying $f\left(x+y^2\right)+1+2x=f\left(x\right)+f\left(y^2\right)+2xf\left(y\right) \forall x\mathit{,}y\mathit{\in }R$, then which of the following statements is true?

Let $y=f\left(x\right)$ be an even function defined on the real number $R$. If $f^{\prime }\left(5\right)=-\frac{1}{\sqrt{3}}$, then the angle made by the tangent to the curve $y=f\left(x\right)$ at $x=-5$ with positive direction of $x-$axis is equal to