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Think about the domain of a radical function that has a difference of a variable and some number under the square root. Keep in mind that it is not possible to calculate a square root of a negative number.
Yes, see solution.
Positive:& sqrt(2), sqrt(5), sqrt(81) ✓ Negative:& sqrt(- 2), sqrt(- 8), sqrt(- 19) * The set of values of the independent variable is called a domain. We conclude that the domain of y=sqrt(x) is limited to x≥ 0. Now, let's find the domains of the other two square root functions. y=sqrt(x+5) and y=sqrt(x-3) In order to do this, we will use the fact that the radicand of a square root function should be a non-negative number. We can form two inequalities to find these domains.
Function | y=sqrt(x+5) | y=sqrt(x-3) |
---|---|---|
Inequality | x+5≥ 0 | x-3≥ 0 |
Solution | x≥ - 5 | x≥ 3 |