1. ## domain/range help

Hey guys, I'm having a problem with finding the domain and range of this function:

f(x) = sqrt(X^2 - 1)

this is what i thought:
x|xER
y|yER, y≥1

but when you substitute 1 for x, you get y = 0, so it disproves what I thought to be correct.

the second one I need help with is the function:

f(x) = sqrt(x^2 - 1)/x-1

i have no idea what the domain/range for that function could be, i've never seen something like that.

2. $f(x) = \sqrt{x^2 - 1}$

In order for the square root to be defined, $x^2 - 1$ must be a nonnegative number. Therefore, the domain is all x such that $x^2 - 1 \geq 0$ (can you put this in terms of intervals?). The range is $y \geq 0$ (why?).

3. hi
the range is $[0,\infty)$.

4. wow thanks for the fast response.

can
$
x^2 - 1 \geq 0
$

be rephrased as

x ≥ sqrt(1) ?

thanks again

5. Originally Posted by snypeshow
wow thanks for the fast response.

can
$
x^2 - 1 \geq 0
$

be rephrased as

x ≥ sqrt(1) ?

thanks again
Not exactly. You have $x^2 \geq 1$, which leads to the inequality $|x| \geq 1$. In summary: x can be negative.

6. so would it be best to leave it as
$x^2 - 1 \geq 0$?

i also need help with:

f(x) = sqrt(x^2 - 1)/x-1

for domain and range

7. Originally Posted by snypeshow
so would it be best to leave it as
$x^2 - 1 \geq 0$?
The best way to write it would be $x \leq -1$ or $x \geq 1$.