Question

What is the domain of the function? y=(√5x-10)
What is the range of the function? y=(√x+2)-6
Please explain!!

Answer 1

is it
\[f(x)=\sqrt{5x-10}\]?

Answer 2

The question said y=

Answer 3

yeah, because it was written by an idiot, this beginning the life long confusion between a function and an equation
no problem we can still solve if

Answer 4

Ok

Answer 5

you cannot take the square root of a negative number, so your job here is to solve
\[5x-10\geq 0\] for \(x\) which takes only two steps

Answer 6

add 10, divide by 5 and get
\[5x-10\geq 0\\
5x\geq 10\\
x\geq 2\] is your domain

Answer 7

Ok that makes sense

Answer 8

for the second one, is it
\[y=\sqrt{x+2}-6\]?

Answer 9

yes

Answer 10

in this case you are looking for the possible \(y\) values, not the \(x\) values
it is always the case that \(\sqrt{\text{whatever}}\geq 0\) and so
\[\sqrt{\text{whatever}}-6\geq -6\]
your range is \(y\geq -6\)

Answer 11

Ok, Thanks! Your explanations made alot of sense!

Answer 12

yw, glad to help

Answer 13

now don't tell your math teacher, but \(y=expression\) is not a function, it is an equation
also don't tell him or her that you do not "find" the domain of a function, you should be told the domain of a function; it is part of the definition
we will keep that between us

Answer 14

Ok :)