Question

Combine like terms in the equation f(x)=-f(x)_______=0

Answer 1

Given

`f(x)=-f(x)`

We can sum f(x) on both sides, and we will get

`f(x)+f(x)=-f(x)+f(x)_{}`

But -f(x) + f(x) = 0, then

`f(x)+f(x)=0`

Now we can combine the terms and we get

`2\cdot f(x)=0`

Divide both sides by 2

`f(x)=0`

And here we have solved our problem. That's the only function that is odd and even at the same time, the graph of this function is basically the x-axis because it's a constant in y = 0, we can see even and odd because

`f(x)=0,\forall x\in\R`

Therefore

`\begin{gathered} f(x)=0=f(-x) \\ \\ f(x)=0=-f(x) \end{gathered}`

Odd and even at the same time.