# Thread: Finding Domain and Range

1. ## Finding Domain and Range

What are the general rules for finding domain and range? Walk me through...

Find Domain:

f(x)= sqrt(4-x)/(x+1) (x^2+1)

Find Range:

f(x)= 5+sqrt(4-x)

2. Originally Posted by renae
What are the general rules for finding domain and range? Walk me through...

Find Domain:

f(x)= sqrt 4-x/(x+1) (x^2+1)
$\frac{\sqrt{4-x}}{(x+1)(x^2+1)}$

Now $4-x\geq 0 \mbox { and }x\not = -1$.

3. Yeah, I know that, but how would I write it?
I have down:

(-inf, 4) U (4,0)

which i know to be completely and utterly wrong, but I just get so confused on trying to write those.

4. From $4-x\geq 0$ we get $x\leq 4$ or $x\in(-\infty,4]$.
But $x\neq -1$ (else the denominator is 0).
So, we must eliminate -1 from the interval.
Then $x\in(-\infty,4]-\{-1\}$ or $x\in(-\infty,-1)\cup(-1,4]$

5. Originally Posted by renae
Find Range:

f(x)= 5+sqrt(4-x)
$\sqrt{4-x}\geq 0,\forall x\leq 4\Rightarrow 5+\sqrt{4-x}\geq 5,\forall x\leq 4$
Then the range is $[5,\infty)$