Answer with Step-by-step explanation:
Even function: If f(x)=f(-x)
Then, the function is an even function.
Odd function: If [tex]f(x)\neq f(-x)[/tex]
Then, the function is an odd function.
a.[tex]f(x)=x^5+x[/tex]
Replace x by -x
[tex]f(-x)=(-x)^5+(-x)=-x^5-x=-(x^5+x)[/tex]
[tex]f(x)\neq f(-x)[/tex]
Hence, the function is an odd function.
b.[tex]g(x)=1-x^6[/tex]
Replace x by -x
[tex]g(-x)=1-(-x)^6=1-x^6[/tex]
[tex]g(x)=g(-x)[/tex]
Hence, g(x) is an even function.
c.[tex]h(x)=2x-x^4[/tex]
Replace x by -x
[tex]h(-x)=2(-x)-(-x)^4=-2x-x^4[/tex]
[tex]h(x)\neq h(-x)[/tex]
Hence, h(x) is an odd function.
