An expression is well-defined if you can compute its value without any illegal operations. Examples of expressions that are not well-defined include 
and 
. For what values of 
is the expression
well-defined?
Please enter your response in interval notation. Refer to Formatting Tips below for detailed instructions on formatting your response.
+23254 Taking the parts individually:
√(x + 1) is well-defined when x + 1 ≥ 0 ---> x ≥ -1 (x + 1 must be zero or positive)
√(1 - x) is well-defined when 1 - x ≥ 0 ---> -x ≥ -1 ---> x ≤ 1 (1 - x must be zero or positive)
√(x) is well-defined when x > 0 (x can't be 0 because it is in the denominator)
Since x > 0 and x ≥ -1 ---> x > 0
x > 0 and x ≤ 1 ---> (0, 1]
+23254 Taking the parts individually:
√(x + 1) is well-defined when x + 1 ≥ 0 ---> x ≥ -1 (x + 1 must be zero or positive)
√(1 - x) is well-defined when 1 - x ≥ 0 ---> -x ≥ -1 ---> x ≤ 1 (1 - x must be zero or positive)
√(x) is well-defined when x > 0 (x can't be 0 because it is in the denominator)
Since x > 0 and x ≥ -1 ---> x > 0
x > 0 and x ≤ 1 ---> (0, 1]
