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

The function is neither even nor odd.

Step-by-step explanation:

the function is even if f(-x) = f(x)

The function is odd if f(-x) = -f(x)

We are given the function:

f(x) = 3(x-1)^4

Solving

f(x) = 3(x^4 -4x^3+6x^2-4x+1)

f(x) = 3x^4-12x^3+18x^2-12x+3

Now putting -x instead of x i,e f(-x)

f(-x) = 3(-x)^4-12(-x)^3+18(-x)^2-12(-x)+3

Solving

f(-x) =3x^4+12x^3+18x^2+12x+3

so, f(-x) ≠ f(x) The function is not even

and f(-x) ≠ -f(x) The function is not odd

Hence the function is neither even nor odd.

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