Answered

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

Sagot :

Given

[tex]f(x)=-f(x)[/tex]

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

[tex]f(x)+f(x)=-f(x)+f(x)_{}[/tex]

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

[tex]f(x)+f(x)=0[/tex]

Now we can combine the terms and we get

[tex]2\cdot f(x)=0[/tex]

Divide both sides by 2

[tex]f(x)=0[/tex]

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

[tex]f(x)=0,\forall x\in\R[/tex]

Therefore

[tex]\begin{gathered} f(x)=0=f(-x) \\ \\ f(x)=0=-f(x) \end{gathered}[/tex]

Odd and even at the same time.

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