Which of the following is an odd function? g(x) = x2 g(x) = 5x – 1 g(x) = 3 g(x) = 4x

Question

Which of the following is an odd function?

g(x) = x2
g(x) = 5x – 1
g(x) = 3
g(x) = 4x

in progress 0
2022-07-23T02:25:08+00:00 2 Answers 0

Answers ( 2 )

  1. Vivian
    0
    2022-07-23T02:26:27+00:00

    An odd function is symmetrical about the origin: g(-x) = -g(x).

    The 4th selection is appropriate.

  2. Olivia
    0
    2022-07-23T02:26:44+00:00

    Answer:

    g(x) = 4x is an odd function.

    Step-by-step explanation:

    A function g(x) is odd if it satisfies that, for all x we have g(-x) = -g(x). Then,

    [tex]g(x) =x^2[/tex] is not an odd function beacuse only give positive values, then for example if x= 2

    [tex]g(-2) =(-2)^2 = 4 neq -4 = -g(2)[/tex].

    g(x) = 5x-1 is not an odd function. I’ll also give you a counterexample: for x=1 we have

    g(-1) = 5(-1)-1 = -6 u2260 -4 = -(5-1) = -g(1).

    g(x) = 3 is not an odd function. I’ll also give you a counterexample: for x=1 we have

    g(-1) = 3 u2260 -3 = -g(1).

    Finally, g(x) = 4x is an odd function because for all x we have g(-x) = -g(x):

    g(-x) = 4(-x) = -4x = -g(x).

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