Question

Пожалуйста! Найдите область определения y=5/корень из(х^2-5x-14)

Answer 1

Подкоренное выражение должно быть неотрицательным, знаменатель дроби не может равняться нулю. Эти условия приводят к выражению
х²-5х-14 > 0
D=25+56=81
x=(5-9)/2=-2    или    x=(5+9)/2=7
\\\\\\\\\\\\\\\\                          /////////////////////
-----------(-2)----------------(7)----------→
Ответ. (-∞; -2)U(7; +∞)

Answer 2

Finding the Domain of y=5/sqrt(x^2-5x-14)

To find the domain of the function y=5/sqrt(x^2-5x-14), we need to determine the values of x for which the function is defined. The square root of a negative number is not real, so we need to ensure that the expression inside the square root is non-negative.

The expression inside the square root, x^2-5x-14, should be greater than or equal to 0 for the function to be defined.

Calculating the Domain

To find the domain, we can solve the inequality x^2-5x-14 ≥ 0.

The solutions to this inequality will give us the range of x values for which the function is defined.

Solution

The solutions to the inequality x^2-5x-14 ≥ 0 are x ≤ -2 and x ≥ 7.

Therefore, the domain of the function y=5/sqrt(x^2-5x-14) is x ≤ -2 or x ≥ 7.

This means that the function is defined for all x values less than or equal to -2 and all x values greater than or equal to 7.

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