Question

Can you correct me theses answers? Just want to know which one is wrong

Answer 1

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

`f(x)=\lvert x\rvert`

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

`f(x)=(x^3+x)/(3+x^2)`

we have that

f(-x)=-f(x) -----> is a odd function

N 4

we have

`f(x)=\lvert x\rvert x`

Verify if the function is odd

`\begin{gathered} f(-x)=\lvert-x\rvert(-x)=-x^2 \\ -f(x)=-x^2 \end{gathered}`