Question

Область визначення функції y= 3 —————- X2+5x

Answer 1

(5х +х ²)≠0

х*(5+х)≠0

х≠0; х≠-5

Answer 2

To determine the domain of the function $y = \frac{3}{{x^2 + 5x}}$, we need to consider the values of $x$ for which the function is defined. The domain of a function is the set of all real numbers $x$ for which the expression is valid, and the denominator of the fraction cannot be equal to zero since division by zero is undefined.

In this case, the denominator $x^2 + 5x$ cannot be equal to zero. So, to find the domain, we need to solve the equation:

$x^2 + 5x = 0$

Factorizing the equation:

$x(x + 5) = 0$

Setting each factor to zero and solving for $x$:

$x = 0$ or $x + 5 = 0$

$x = 0$ or $x = -5$

These are the points where the function is not defined, as the denominator becomes zero at these values. Therefore, the domain of the function is all real numbers except $x = 0$ and $x = -5$. In interval notation, the domain can be written as:

Domain: $(- \infty, -5) \cup (-5, 0) \cup (0, \infty)$