Step-by-step explanation:
An odd function is where g(x) = -g(-x).
Therefore the answer is g(x) = 4x, as it passes through the origin and g(x) is positive when x is positive, and g(x) is negative when x is negative.
The odd function will be g(x) = 4x. Then the correct option is D.
A true function f(x) is said to be an odd function if the output value of f(-x) is the same as the negative of f(x) for all values of x in the domain of f.
The equation should be stored in an odd function:
f(-x) = -f(x)
Let's check all the options.
A. The function is g(x) = x².
Substitute x = -x, then we have
g(x) = (-x)²
g(x) = x²
This is an even function.
B. The function is g(x) = 5x – 1.
Substitute x = -x, then we have
g(x) = 5(–x) – 1
g(x) = – (5x + 1)
This is a neither even nor odd.
C. The function is g(x) = 3.
Substitute x = -x, then we have
g(x) = 3
This is an even function.
D. The function is g(x) = x.
Substitute x = -x, then we have
g(x) = -x
g(x) = x
This is an odd function.
Then the correct option is D.
More about the odd function link is given below.
https://brainly.com/question/14264818
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