Question

Which value of x is in the domain of f(x)=√x - 6? a) x= 0 b) x= 5 c) x= 10 d) x=-4

Answer 1

The value of x that is in the domain of f(x)=√x - 6 is x = 10, because it is the only provided value that is greater than or equal to 6.

The given function is f(x)=√x - 6. The domain of a function is the set of all possible input values (in this case, x-values) that will output a real number. For square root functions, the radicand (the value under the square root) cannot be negative, because the square root of a negative number is not a real number.

This means the value inside the square root (√x) must be greater than or equal to zero. So, x must be greater than or equal to 6. So, let's look at the options:

1. x= 0, this value does not satisfy x ≥ 6.
2. x= 5, this value also does not satisfy x ≥ 6.
3. x= 10, this value does satisfy x ≥ 6.
4. x=-4, this value does not satisfy x ≥ 6.

Therefore, the value of x that is in the domain of f(x) = √x -6, is x = 10.

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