SOLUTION: Im in Pre-Calc. What is the domain of: h(x) = square root of (4-x) ALL OVER (x+1)(x squared+1) give answers like (-3, 1) U (1, infinity)

SOLUTION: Im in Pre-Calc. What is the domain of: h(x) = square root of (4-x) ALL OVER (x+1)(x squared+1) give answers like (-3, 1) U (1, infinity) - that is just an answer from a prev

Question 486971: Im in Pre-Calc. What is the domain of:
h(x) = square root of (4-x) ALL OVER (x+1)(x squared+1)
give answers like (-3, 1) U (1, infinity) - that is just an answer from a previous problem
im having trouble with this current one because not much makes sense - thanks for the help
Found 3 solutions by John10, jim_thompson5910, MathLover1:
Answer by John10(297)   (Show Source): You can put this solution on YOUR website!
Try to find the RESTRICTED value which make the denominator to be zero
set the denominator to be zero:
(x + 1)(x^2 + 1) =0
Since x^2 + 1 is NEVER to be zero.
so x + 1 = 0
x = -1
Thus the domain is all REAL NUMBERS EXCEPT -1
D = {x|(-inf, -1)U (-1, inf)}
John10:)
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
You cannot divide by zero. So the denominator cannot be equal to zero. If it were, then

which means that

or

Solve the first equation to get . Solve the second equation to get or .

Ignore the last two answers (since we're only concerned about real numbers).

So if , then the entire denominator is zero.

So we must exclude this value from the domain.

So the domain is

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

denominator cannot be equal to
so, if either or equal to denominator will be
what values for are NOT solutions, we will find out if we make denominator equal to
if
....->...
or
if
....->.......>...=+-...imaginary roots

so, you have real solution
(, ) U (, )

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