Even and Odd Functions

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.

The function $f\left(x\right)=3x^3$ is symmetric with respect to the $y$-axis.

The function $f\left(x\right)=x^3$ is symmetric with respect to the $y$-axis.

The function $f\left(x\right)=3x^3$ is symmetric with respect to the $y$-axis.

The function $f\left(x\right)=x^3$ is symmetric with respect to the $y$-axis.

If $f:\left[- 4,0\right]\to R$ is defined by $f\left(x\right)=e^x+\sin x$, its even extension to $\left[- 4,4\right]$ is given by:

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

Show that, $f(x)=\log \left(x+\sqrt{1+x^{2}}\right)$ is an odd function.

State whether the following statements are true/false:

State whether the following statements are true/false:

State whether the following statements are true/false:

[v] If a function is not even, then it must be an odd function.