Question

Determina si las siguientes funciones son pares, impares o ninguna

a. f(x) = 4x^2 - Even
b. g(x) = x^4 + 3x^2 - x - Even
c. h(x) = x^2 + 5x + 1 - Neither
d. f(x) = x^4 - 12x^2 - Even
e. h(x) = x^5 + 3x^4 - Odd
f. g(x) = -2x^6 + x^2 - Even

Answer 1

An even function times an even function produces an even function, while an odd function times an odd function produces an even function. However, an odd function times an even function can produce an odd or neither function.

Step-by-step explanation:

In general, an even function times an even function produces an even function. A simple example of an even function is the product x² e-x² (even times even is even).

Similarly, an odd function times an odd function produces an even function, such as x sin x (odd times odd is even). However, an odd function times an even function can produce an odd or neither function.