Determine algebraically whether the function g (x) = x^2 is even odd or neither

Question

Mathematics

Charity Gilmore

12 April, 08:23

Determine algebraically whether the function g (x) = x^2 is even odd or neither

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Answers (2)

Know the Answer?

Pittman · Answer 1

I think its 2 because its 2 so you will put 2

Giada Cantrell · Answer 2

g (x) = x^2

g (-x) = (-x) ^2 ... replace every x with - x

g (-x) = x^2 ... squaring a negative makes it positive

So because g (x) = g (-x) for every x, this means g (x) is an even function. For polynomials, if every exponent is even, then the entire polynomial is even as well.

Note: if a function is even, then it won't be odd or vice versa unless the function is the zero function. In other words, g (x) = 0 is both even and odd.