Question

which of the following is an odd function?

Answer 1

number 3 is an odd function

Answer 2

Answer:

The odd function is D) $g(x)=4x$

Step-by-step explanation:

We need to check given options are odd function or not

Since, odd function is satisfy the f(-x) = -f(x)

Check for part A) $g(x)=x^{2}$

Replace x by - x in $g(x)=x^{2}$

$g(-x)=(-x)^{2}$

$g(-x)=x^{2}$

since, we can not write it as $g(-x) = -g(x)$

Hence, this is not an odd function

Check for part B) $g(x)=5x-1$

Replace x by - x in $g(x)=5x-1$

$g(-x)=5(-x)-1$

$g(x)=-5x-1$

since, we can not write it as $g(-x) = -g(x)$

Hence, this is not an odd function

Check for part C) $g(x)=3$

since, constant functions are even function

Hence, this is not an odd function

Check for part D) $g(x)=4x$

Replace x by - x in $g(x)=4x$

$g(-x)=4(-x)$

$g(x)=-4x$

$g(x)=-g(x)$

since, we can write it as $g(-x) = -g(x)$

Hence, this is an odd function

Therefore, the odd function is D) $g(x)=4x$