Question

What are the domain and range of the function?

f(x)=x−1−−−−√3



Responses

Domain: [1, ∞)
Range: [0, ∞)



Domain: [ 1 , ∞ ) , , Range: left square bracket 0 comma infinity right parenthesis, , ,

Domain: ​​[1, ∞)

Range: ​(−∞, ∞)​



Domain: ​ ​ left square bracket 1 comma infinity right parenthesis, , Range: ​ left parenthesis negative infinity comma infinity right parenthesis ​, , ,

Domain: (−∞, ∞)

Range: (−∞, ∞)



Domain: left parenthesis negative infinity comma infinity right parenthesis, , Range: left parenthesis negative infinity comma infinity right parenthesis, , ,

Domain: [0, ∞)

Range: [1, ∞)

Answer 1

The domain and range of the function f(x) = sqrt(x - 1) are [1, ∞) and [0, ∞) respectively. The domain is determined by the requirement that the square root's argument must be non-negative, and the range is based on the output values of a square root function, which are always non-negative.

Step-by-step explanation:

The function f(x) = √{x - 1} can be analyzed to determine its domain and range. To find the domain, we look for all x-values for which the function is defined. Since the function involves a square root, the expression inside the square root must be non-negative.

Hence, x - 1 ≥ 0 which simplifies to x ≥ 1.

Therefore, the domain of the function is [1, ∞).

As for the range, since the square root function produces non-negative results for non-negative inputs, and considering the domain starting at 1, the smallest value of f(x) is 0 when x = 1. As x increases, the value of f(x) also increases without bound.

Thus, the range of the function is [0, ∞).