Question

Write Domain/Range:

f(x)= √x-1

Answer 1

is the square root on the x-1 like this: sqrt(x-1)?

Answer 2

yes its over both x and -1

Answer 3

\[f(x)=\sqrt{x-1}\]

Answer 4

you can't take the square root of a negative, so find where x-1 starts being negative, which is at zero.

So x-1 = 0
x = 1

Now test values

can you put a number greater than 1 in?
what about 1?
what about less than 1?

Answer 5

Since only values less than 1 (like -2) make the value under the square root negative, then the domain is x is greater than or equal to 1.

Answer 6

so would it be (1,\[\infty \])

Answer 7

no, use square brackets on the 1, because that indicates including 1, like this:
[1, infiity)
use the parenthesis on infinity because you can't really include it.

Answer 8

gotcha.. then how do i get the range?

Answer 9

The easiest way is to graph it
The second easiest way is to consider it a transformation of sqrt(x)
The hardest way is to find the domain of the inverse

On the graph, it goes up from zero. Range is the possible y values it can ever have.

With the second way, you know that the range of sqrt(x) is [0, infinity) and subtracting from x shifts it horizontally so that doesn't change it.

The third way is annoying, so just go with that.

Answer 10

okay, so if i dont need to graph i can just make the range [0, infin)

Answer 11

Yup