Answered

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Determine algebraically if f(x)=x^2-8 is a function even, odd, or neither.

Sagot :

For a function to be even, it has to meet the following condition:

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

To check if the given is an even function, evaluate the function at x and -x:

[tex]\begin{gathered} f(x)=x^2-8 \\ f(-x)=(-x)^2-8=x^2-8 \\ f(x)=f(-x) \end{gathered}[/tex]

It means that the function is even.

For a function to be odd, it has to meet this condition:

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

We already know the values of f(-x) and f(x) and from this we can state that the function is not odd.

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