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 All 2 months 2022-07-23T02:25:08+00:00 2022-07-23T02:25:08+00:00 2 Answers 0
Answers ( 2 )
An odd function is symmetrical about the origin: g(-x) = -g(x).
The 4th selection is appropriate.
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).