Question

Determine algebraically ifthe function is even, odd, or neither. f(x)=5

Answer 1

Given:

The function is,

$f(x)=5$

To determine the function is even or odd, replace x by -x,

$\begin{gathered} f(x)=5 \\ f\mleft(-x\mright)=5 \\ \Rightarrow f(x)=f(-x) \end{gathered}$

Moreover, the given function is constant function. and the graph of the function is symmetric about y axis.

Also, if f(-x)=-f(x) then function is odd , if f(-x)=f(x) then function is even.

Hence, from above discussion it is clear that the given function is even.