Given equation: y = √25 - x^2
The domain of this equation is all real values of x such that √25 - x^2 is defined.
Step 1: Write the equation in terms of x only so that we can identify the domain:
y = √25 - x^2
=> x^2 = √25 - y
=> x = √(√25 - y)
Step 2: Since "√25-y" must be greater than or equal to 0 for the equation to be defined, we can set the inequality to find the domain for x as:
√25 - y ≥ 0
=> -y ≥ -√25
=> y ≤ √25
Therefore, the domain for the equation y = √25 - x^2 is all real values of x such that y is less than or equal to √25. Represented in the standard form of intervals, this can be written as:
Domain: x ∈ (-∞, +∞) and y ∈ [0, √25]