Question

Determine whether the function f(x) = 3(x − 1)4 is even or odd.

Answer 1

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 2

Answer:

The given function is odd

Step-by-step explanation:

we need to determine the function $f(x)=3(x-1)^{4}$ is odd or even

Since, A function f(x) is said to be even if $f(-x) = f(x)$

and f(x) is said to be odd if $f(-x)= - f(x)$ and $f(-x) \neq f(x)$

We Replace x with -x in the given function and solve;

$f(x)=3(x-1)^{4}$

$f(-x)=3(-x-1)^{4}$

take out the negative common,

$f(-x)=3[-(x+1)]^{4}$

Since $(-1)^{4}=1$

$f(-x)=3(x+1)^{4}$

$f(-x) \neq f(x)$

Hence, the given function is odd