Remember that
A function is an even function if f of x is equal to f of −x for all the values of x
and
f(x) is an odd function when f(-x) = -f(x)
Verify each function
N 1
we have
[tex]f(x)=\lvert x\rvert[/tex]we have that
f(x)=f(-x) -----> that means even function
N 2
we have
f(x)=2
so
f(x)=f(-x) ---> that means even function
N 3
we have
[tex]f(x)=\frac{x^3+x}{3+x^2}[/tex]we have that
f(-x)=-f(x) -----> is a odd function
N 4
we have
[tex]f(x)=\lvert x\rvert x[/tex]Verify if the function is odd
[tex]\begin{gathered} f(-x)=\lvert-x\rvert(-x)=-x^2 \\ -f(x)=-x^2 \end{gathered}[/tex]