contestada

Which statement best describes how to determine whether f(x) = 9 – 4x2 is an odd function?

A. Determine whether 9 – 4(–x)2 is equivalent to 9 – 4x2.
B. Determine whether 9 – 4(–x2) is equivalent to 9 + 4x2.
C. Determine whether 9 – 4(–x)2 is equivalent to –(9 – 4x2).
D. Determine whether 9 – 4(–x2) is equivalent to –(9 + 4x2).

Respuesta :

Answer:

Option C - determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.

Step-by-step explanation:

To find : Which statement best describes how to determine whether [tex]f(x) = 9-4x^2[/tex] is an odd function?

Solution :

We have a property for odd functions,

Let f(x) be an odd function then it must satisfy

[tex]f(-x)= -f(x)[/tex]

Now, we have been given the function [tex]f(x) = 9-4x^2[/tex]

For this function to be odd, it must satisfy the above property.

Replace x with -x,

[tex]f(-x)=9-4(-x)^2[/tex]

and

[tex]-f(x)=-(9-4x^2)[/tex]

Hence, in order to the given function to be an odd function, we must determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.

Therefore, C is the correct option.

Otras preguntas