Question

Найти область определения функции у= корень из х+4 + корень из 2х+3

Answer 1

Подкоренные выражения должны быть больше либо равны нулю

Answer 2

Если вы имели ввиду квадратный корень,то вот...

Answer 3

Finding the Domain of the Function y = √(x^4) + √(2x^3)

To find the domain of the function y = √(x^4) + √(2x^3), we need to determine the values of x for which the function is defined. The domain of a function is the set of all possible input values (x) for which the function produces real output values (y).

The function y = √(x^4) + √(2x^3) involves square roots, and the radicand (expression under the square root) must be non-negative for real number outputs. Therefore, we need to consider the domain of each individual square root expression.

1. Domain of √(x^4): - The expression inside the square root, x^4, is a fourth power, which means it is always non-negative for real numbers. Therefore, the domain of √(x^4) is all real numbers.

2. Domain of √(2x^3): - The expression inside the square root, 2x^3, must also be non-negative for real outputs. This means that 2x^3 ≥ 0, which implies x ≥ 0. Therefore, the domain of √(2x^3) is all real numbers greater than or equal to 0.

Combining the Domains

Since both √(x^4) and √(2x^3) have domains of all real numbers, the combined domain of the function y = √(x^4) + √(2x^3) is also all real numbers.

Therefore, the domain of the function y = √(x^4) + √(2x^3) is all real numbers. This means that the function is defined for any real value of x.