simonhogue3580
contestada

Determine whether the function f(x) = 3x4 is even or odd.

The function is even because f(x) = f(−x).
The function is odd because f(x) = f(−x).
The function is even because −f(x) = f(x).
The function is odd because −f(x) = f(x).

Respuesta :

calculista

Answer:

The function is even because f(x) = f(−x).

Step-by-step explanation:

we know that

An even function is one for which  

f (−x)=f(x) for all x in its domain.

An odd function is one for which  

f( −x) =−f(x) for all x in its domain

In this problem we have

[tex]f(x)=3x^{4}[/tex]

so

[tex]f(-x)=3(-x)^{4}=3x^{4}[/tex]

therefore

f (x)=f(-x) for all x in its domain.

Is a even function

Answer:

Option A) The function is even because f(x) = f(−x).

Step-by-step explanation:

We are given the following in the question:

[tex]f(x) = 3x^4[/tex]

We have to check whether the given function is odd or even.

Even function:

  • [tex]f(-x) = f(x)[/tex]

Odd function:

  • [tex]f(-x) = -f(x)[/tex]

To check, we evaluate f(-x)

[tex]f(x) = 3x^4\\f(-x) = 3(-x)^4 = 3(-1)^4(x)^4 = 3x^4 = f(x)[/tex]

Thus, the given function is even.

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