Determine algebraically whether or not the function f(x)=3x^2/1-x^4, is even or odd and justify your answer

A. The function is odd because f(-x) = -f(x)

B. The function is odd because f(-x) = f(x)

C. The function is even because f(-x) = -f(x)

D. The function is even because f(-x) = f(x)

E. The function is neither even nor odd because because f(-x) does not equal f(x) and f(-x) does not equal -f(x)

Respuesta :

Answer:

D

Step-by-step explanation:

If the function is even then

f(x) = f(- x)

Given

f(x) = [tex]\frac{3x^2}{1-x^4}[/tex] then

f(- x) = [tex]\frac{3(-x)^2}{1-(-x)^4}[/tex] = [tex]\frac{3x^2}{1-x^4}[/tex]

Since f(x) = f(- x) then f(x) is even

Answer: D

Step-by-step explanation: