Question

24 балла Область определения x^3+5x^2-9; y=4/x^2+x-72; y=√4x-5 ( в корне, если знак не понять )

Answer 1

Решение задания смотри на фотографии

Answer 2

Finding the Domain of x^3 + 5x^2 - 9

To find the domain of the function x^3 + 5x^2 - 9, we need to determine the values of x for which the function is defined. The domain of a polynomial function is all real numbers, so there are no restrictions on the values of x for this function.

Domain of x^3 + 5x^2 - 9: The domain is all real numbers.

Analyzing the Equations y = 4/x^2 + x - 72 and y = √(4x - 5)

Let's analyze the equations y = 4/x^2 + x - 72 and y = √(4x - 5) to understand their properties and solutions.

Equation 1: y = 4/x^2 + x - 72 - This equation represents a rational function. - The domain of a rational function excludes any x-values that make the denominator equal to zero. - To find the domain, we need to solve the equation x^2 = 0 to identify any restrictions on x.

Equation 2: y = √(4x - 5) - This equation represents a square root function. - The domain of a square root function includes only the values of x that make the expression inside the square root non-negative.

Finding the Domain of y = 4/x^2 + x - 72

To find the domain of the rational function y = 4/x^2 + x - 72, we need to consider the restrictions on x that make the denominator non-zero.

Domain of y = 4/x^2 + x - 72: The domain is all real numbers except for the values of x that make the denominator equal to zero.

Finding the Domain of y = √(4x - 5)

To find the domain of the square root function y = √(4x - 5), we need to consider the values of x that make the expression inside the square root non-negative.

Domain of y = √(4x - 5): The expression inside the square root, 4x - 5, must be greater than or equal to zero.

Conclusion

- The domain of the function x^3 + 5x^2 - 9 is all real numbers. - The domain of the rational function y = 4/x^2 + x - 72 is all real numbers except for the values of x that make the denominator equal to zero. - The domain of the square root function y = √(4x - 5) is the set of all real numbers that make the expression inside the square root non-negative.