Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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.