A function is considered odd when [tex]f(-x)=-f(x)[/tex]
So, let us check each function
[tex]f(-x)=3(-x)^2-x\\\Rightarrow f(-x)=3x^2-x\neq -f(x)[/tex]
[tex]f(-x)=4(-x)^3+7\\\Rightarrow f(-x)=-4x+7\neq -f(x)[/tex]
[tex]f(-x)=5(-x)^2+9\\\Rightarrow f(-x)=5x+9\neq -f(x)[/tex]
[tex]f(-x)=6(-x)^3+2(-x)\\\Rightarrow f(-x)=-6x^3-2x\\\Rightarrow f(-x)=-(6x^3+2x)=-f(x)[/tex]
Hence, the last option is an odd function.
Learn more:
https://brainly.com/question/15775372
https://brainly.com/question/14302660
