Question

Y=√16-x^2найти область определения функции

Answer 1

....................................

Answer 2

To find the domain of the function Y = √(16 - x^2), we need to identify the values of x for which the function is defined. The square root function (√) is only defined for non-negative values or zero, as the square root of a negative number is not a real number.

In our case, we have Y = √(16 - x^2), so we need to ensure that the expression inside the square root is non-negative:

16 - x^2 ≥ 0

Now, let's solve for x:

x^2 ≤ 16

To find the solutions for x, we take the square root of both sides. Remember that when we take the square root, we consider both positive and negative roots:

√(x^2) = √(16)

x ≤ 4 and x ≥ -4

So, the domain of the function is the set of all real numbers that satisfy this inequality: x ∈ [-4, 4].