Answer:
The odd function is D) [tex]g(x)=4x[/tex]
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) [tex]g(x)=x^{2}[/tex]
Replace x by - x in [tex]g(x)=x^{2}[/tex]
[tex]g(-x)=(-x)^{2}[/tex]
[tex]g(-x)=x^{2}[/tex]
since, we can not write it as [tex]g(-x) = -g(x)[/tex]
Hence, this is not an odd function
Check for part B) [tex]g(x)=5x-1[/tex]
Replace x by - x in [tex]g(x)=5x-1[/tex]
[tex]g(-x)=5(-x)-1[/tex]
[tex]g(x)=-5x-1[/tex]
since, we can not write it as [tex]g(-x) = -g(x)[/tex]
Hence, this is not an odd function
Check for part C) [tex]g(x)=3[/tex]
since, constant functions are even function
Hence, this is not an odd function
Check for part D) [tex]g(x)=4x[/tex]
Replace x by - x in [tex]g(x)=4x[/tex]
[tex]g(-x)=4(-x)[/tex]
[tex]g(x)=-4x[/tex]
[tex]g(x)=-g(x)[/tex]
since, we can write it as [tex]g(-x) = -g(x)[/tex]
Hence, this is an odd function
Therefore, the odd function is D) [tex]g(x)=4x[/tex]
