Question

How do you tell if a function is odd even or neither $?$

Answer 1

Describing function as odd and even:

Even Function: a function, $f\left(x\right)$ is even if $f\left(x\right)=f(-x)$

Odd Function: a function, $f\left(x\right)$ is odd if $f\left(x\right)=-f\left(x\right)$

Now, let assume a function $f\left(x\right)=\tan x+secx$

$\begin{array}{rcl}f(-x)& =& \tan (-x)+sec(-x)\\ & =& –\tan x+secx\\ & \ne & -f\left(x\right)orf(-x)\end{array}$

$\therefore f\left(x\right)$ is neither even nor odd.

Hence, we can tell the function is odd, even or neither by the conditions stated above.