You can put this solution on YOUR website!
Please put parentheses around numerators, denominators and radicands (expressions within a radical are called radicands). The way you posted this question could be interpreted as:
Technically, the way you posted the function, the correct interpretation is the first one. The way to post the other three, in order are:
h(y) = 2y +9/(sqrt(y) + 5)
h(y) = (2y +9)/sqrt(y) + 5
h(y) = (2y +9)/sqrt(y + 5)
Without knowing which equation is right and not wanting to do all four, I can only give you general help:
- Radicands of square roots must be non-negative (positive or zero). So you will solve the inequality
- Denominators must not be zero. Any value for y that makes a denominator zero, if any, must be removed from the domain.
So your domain will be the solution to:
"minus" any numbers that make the denominator zero, if any.
If this general help is not enough for you to be able to find the domain on your own, then please repost your question.
BTW It is good that you recognized the irrational denominator. But this denominator was given to you. It was not one you came up with. When an expression is given to you this way then don't worry about rationalizing the denominator. Just rationalize any answers you figure out.