Question

If f (x) = startroot one-half x minus 10 endroot 3, which inequality can be used to find the domain of f(x)? startroot one-half x endroot greater-than-or-equal-to 0 one-half x greater-than-or-equal-to 0 one-half x minus 10 greater-than-or-equal-to 0 startroot one-half x minus 10 endroot 3 greater-than-or-equal-to 0 equation can be simplified to find the inverse of y = 2x2? startfraction 1 over y endfraction = 2 x squared y = one-half x squared –y = 2x2 x = 2y2

Answer 1

The domain of the function f (x) = √ (one-half x - 10) is determined by the inequality one-half x - 10 ≥ 0, as we cannot have negative numbers under the square root in real number domain.

Step-by-step explanation:

The function given is f (x) = √ (one-half x - 10). The domain of a function represents the set of 'x' values that can be inputted into the function without receiving undefined or irrelevant outputs. In this case, we need to set the value within the square root, (one-half x - 10), to be greater than or equal to 0, because a negative value under the square root would result in an undefined real number. Therefore, the inequality to find the domain of f(x) is one-half x - 10 ≥ 0.

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