Question

Type the correct answer in each box. Use numerals instead of words.

The function f(x) = x^(1/2) is transformed to get function w.
w(x) = (3x)^(1/2) - 4
What are the domain and the range of function w?
domain: x ≥ ____
range: w(x) ≤ ____

Answer 1

The domain of function w(x) is x ≥ 4/3 and the range is w(x) ≤ 0.

Step-by-step explanation:

The original function f(x) = x^(1/2) is transformed into the function w(x) = (3x)^(1/2) - 4.

The domain of a square root function is the set of all non-negative real numbers, since we cannot take the square root of a negative number. In this case, since the function w(x) is defined as the square root of (3x) - 4, we need to ensure that 3x - 4 is not negative. Therefore, the domain of w is x ≥ 4/3.

The range of a square root function is the set of all non-negative real numbers. Since w(x) is the square root of a quantity, it can never be negative. Therefore, the range of w is w(x) ≤ 0.