Question

How to find the domain of a function with a square root fraction?

Answer 1

The domain of a real function will be all the places where the denominator isn't zero and the radicand in the square root isn't negative.

So find the places where the denominator vanishes or the square root is of a negative number and exclude those places from the domain.

Answer 2

To find the domain of a function which is a square root fraction, ensure that the value under the square root is greater than or equal to 0, and that the value in the denominator is not equal to zero.

Step-by-step explanation:

When identifying the domain for a function that includes a square root in a fraction (a radical function), you should consider that square root values have restrictions. In mathematics, you can't take the square root of a negative number (in the set of real numbers), so whatever is under the square root must be equal to or greater than 0.

For example, if you have a function such as f(x) = √(x - 3) / (x - 5), first understand that the value under the square root (which is 'x - 3' in this case) should be greater than or equal to 0. Therefore, you would set up an inequality like this: x-3 >= 0, which simplifies to x >= 3. Now, that's half of the solution. The other half is ensuring that the denominator of the fraction (x - 5) does not equal zero, to prevent division by zero. Therefore, x ≠ 5. Combining these two conditions gives you the domain.

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