Question

find the domain of the function algebraically.....(square root 4-x)/((x+1)(x^2+1)

Answer 1

\[\frac{(\sqrt{4-x})}{(x+1)(x^2+1)}\]

Answer 2

Is that it?

Answer 3

The value under the square root must not be negative.

Answer 4

Thus x < 4 is required.

Answer 5

Also, x+1 need not be 0. So x can not be -1.

Answer 6

from the radical we have\[4-x \ge0\]or\[x \le4\]but from the denominator we have\[x \neq1\]if you put all that together you get\[(-\infty,1) \cup(1,4]\]

Answer 7

So the domain is \[ (-\infty, 4] \backslash \{ -1 \} \]

Answer 8

= (-\infty, -1) \cup (-1, 4]

Answer 9

omg thank you guys soooooo much i just wasted an hour watching youtube videos for no reason =] thanks again!!