Answer:
The function is neither even nor odd.
Step-by-step explanation:
Given : Function [tex]f(x)=3(x-1)^4[/tex]
To find : Determine whether the function is even or odd ?
Solution :
Rules to determine the function is even or odd :
If f(x)=f(-x) then the function is even.
If f(x)=-f(x) then the function is odd.
Now, Test for even function
[tex]f(x)=3(x-1)^4[/tex]
[tex]f(-x)=3(-x-1)^4[/tex]
[tex]f(-x)=3(-(x+1)^4[/tex]
[tex]f(-x)=3(x+1)^4[/tex]
[tex]f(x)\neq f(-x)[/tex] so function is not even.
Test for odd function,
[tex]f(x)=3(x-1)^4[/tex]
[tex]-f(x)=-3(x-1)^4[/tex]
[tex]f(x)\neq -f(x)[/tex] so function is not odd.
So, The function is neither even nor odd.
