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

(a) f(x) = x²/√x²+ 1

(b) g(x) = x^3 - √ x- 7

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asked by Zach
  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.

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