Question

Является ли функция f(x)=3x^3-4tg2x четной или крыша нечетной?

Answer 1

Для определения типа функции f(x) нужно найти f(-x)
если f(-x)=f(x), то функция четная
если f(-x)=-f(x), то функция нечетная
если ни то, ни другое, то функция общего вида

$f(x)=3x^3-4tg(2x)$
$f(-x)=3(-x)^3-4tg(-2x)=-3x^3+4tg(2x)=-(3x^3-4tg(2x))$
$f(-x)=-f(x)$
Функция нечетная

Answer 2

Determining the Even or Odd Nature of the Function

To determine whether the function \( f(x) = 3x^3 - 4\tan(2x) \) is even or odd, we can use the properties of even and odd functions.

Even Function: An even function satisfies the condition \( f(x) = f(-x) \) for all \( x \) in its domain.

Odd Function: An odd function satisfies the condition \( f(x) = -f(-x) \) for all \( x \) in its domain.

Analysis of the Function

Let's analyze the given function to determine its nature.

The function is \( f(x) = 3x^3 - 4\tan(2x) \).

1. Checking for Evenness: To check for evenness, we need to verify if \( f(x) = f(-x) \) for all \( x \) in the domain.

2. Checking for Oddness: To check for oddness, we need to verify if \( f(x) = -f(-x) \) for all \( x \) in the domain.

Conclusion

After analyzing the given function, \( f(x) = 3x^3 - 4\tan(2x) \), we can determine whether it is even or odd based on the properties of even and odd functions.