Answer:
f(x) is an odd function
Step-by-step explanation:
Determine whether the function f(x)=4x^3 is even or odd
[tex]f(x)= 4x^3[/tex]
To check whether f(x) is even then f(-x)= f(x)
To check whether f(x) is odd then f(-x)=-f(x)
Plug in x with -x and check whether it is odd or even
[tex]f(x)= 4x^3[/tex]
[tex]f(-x)= 4(-x)^3=-4x^3[/tex]
f(-x) is not equal to f(x). So f(x) is not an even function
[tex]f(x)= 4x^3[/tex]
[tex]f(-x)= 4(-x)^3=-4x^3[/tex]
f(-x) =-f(x)
So it is an odd function
A function can be even or odd.
[tex]\mathbf{f(x) = 4x^3}[/tex] is an odd function.
A function is said to be odd if:
[tex]\mathbf{f(-x) = -f(x)}[/tex]
The function is given as:
[tex]\mathbf{f(x) = 4x^3}[/tex]
Calculate f(-x)
[tex]\mathbf{f(-x) = 4(-x)^3}[/tex]
[tex]\mathbf{f(-x) = -4x^3}[/tex]
Calculate -f(x)
[tex]\mathbf{-f(x) = -4x^3}[/tex]
By comparison:
[tex]\mathbf{f(x) = -f(x) = -4x^3}[/tex]
Hence, [tex]\mathbf{f(x) = 4x^3}[/tex] is an odd function.
Read more about odd and even functions at:
https://brainly.com/question/15775372
