Question

Найти область определения функции: y(x)=3/ x - 1/x^3.

Answer 1

$y(x)=\frac{3}{x}-\frac{1}{x^3}\\\\OOF:\; \; x\ne 0\\\\D(y)=(-\infty ,0)\cup (0,+\infty )$

Answer 2

To find the domain of a function, we need to identify any values of 'x' that would cause the function to be undefined. In this case, we have the function:

y(x) = 3/(x) - 1/(x^3)

The function is made up of two terms: 3/(x) and 1/(x^3). We need to consider the domain restrictions for each term separately.

1. The term 3/(x) is defined for all real numbers except when the denominator (x) becomes zero because division by zero is undefined. So, we need to exclude x = 0 from the domain.

2. The term 1/(x^3) is also defined for all real numbers except when the denominator (x^3) becomes zero. Again, we need to exclude all values of x that make x^3 equal to zero. Since x^3 = 0 has a single solution at x = 0, we also need to exclude x = 0 from the domain.

Now, combining both restrictions, we see that the function y(x) is undefined when x takes the value of 0.

Therefore, the domain (D) of the function y(x) is all real numbers except x = 0:

D = {x ∈ ℝ | x ≠ 0}