Question

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

The function f(x) = x¹/² is transformed to get function m. m(x) = (x+1)¹/² +2

What are the domain and the range of function m? domain: [ ____ , [infinity])
range: [ ____ , [infinity])

Answer 1

The domain of function m is 0 ≤ x ≤ 20 and the range is [2, [infinity)

Step-by-step explanation:

The original function f(x) = x¹/² is transformed to get function m(x) = (x+1)¹/² + 2. To find the domain of function m, we need to consider the domain of the original function f(x). In this case, since the original function is defined for 0 ≤ x ≤ 20, the domain of function m will also be 0 ≤ x ≤ 20.

To find the range of function m, we need to consider the range of the original function f(x). As f(x) is a square root function, the range is all non-negative real numbers. Adding 2 to the values of f(x) will shift the range vertically upwards by 2 units. Therefore, the range of function m will be [2, [infinity).