Answer:
the function is odd
Step-by-step explanation:
A function f(x) is said to be even if f(-x) = f(x)
On the other hand, f(x) is said to be odd if f(-x)≠ f(x).
We plug in -x in place of x in the given function and simplify;
f(-x) = 3(-x-1)^4
f(-x) = 3[-1(x+1)]^4
f(-x) = 3 *(-1)^4 * (x+1)^4
f(-x) = 3(x+1)^4 ≠ f(x)
Therefore, the function given is odd
Answer:
The given function is odd
Step-by-step explanation:
we need to determine the function [tex]f(x)=3(x-1)^{4}[/tex] is odd or even
Since, A function f(x) is said to be even if [tex]f(-x) = f(x)[/tex]
and f(x) is said to be odd if [tex]f(-x)= - f(x)[/tex] and [tex]f(-x) \neq f(x)[/tex]
We Replace x with -x in the given function and solve;
[tex]f(x)=3(x-1)^{4}[/tex]
[tex]f(-x)=3(-x-1)^{4}[/tex]
take out the negative common,
[tex]f(-x)=3[-(x+1)]^{4}[/tex]
Since [tex](-1)^{4}=1[/tex]
[tex]f(-x)=3(x+1)^{4}[/tex]
[tex]f(-x) \neq f(x)[/tex]
Hence, the given function is odd
