Question

Determine whether the functions are even, odd, or neither.

(a) f(x) = x²/√x²+ 1

(b) g(x) = x^3 - √ x- 7

Answer 1

Odd functions are symmetrical about the origin. Let f(x) be an odd function. f(-x) = -f(x). If its an odd function, it will satisfy this condition.

Even functions are symmetrical about that y axis. Let g(x) be an even function. g(-x) = g(x). If its an even function, it will satisfy this condition.

Neither is when it doesn't satisfy the conditions above.

I'll do (a). I'll assuming it's an even function.
g(-x) = g(x)
(-x)^2/sqrt((-x)^2+1) = x^2/sqrt((-x)^2+1)
x^2/sqrt(x^2+1) = x^2/sqrt(x^2+1)
Therefore, it is even.

You can always plug it in your calculator and check for symmetry.