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