avissidep

2021-06-08

What is the domain of
$f\left(x\right)=5\frac{x}{3-(\sqrt{x}-2)}$ ?

bahaistag

Skilled2021-06-09Added 101 answers

That numerator doesn't impose any restrictions, but there are two constraints from the denominator: the whole denominator cannot be 0 and the number inside the radical cannot be negative. Let's look at each in turn.

The denominator cannot be 0 So then we cannot have

So 11 cannot be in the domain.

The number under the radical cannot be negative. That is, we must have

Conclusion

Putting these two conditions together we get that the domain is

Domain