SOLUTION: My book doesn't give much help on solving this. Find the domain of f(x)3x+1/ x^2+4

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Question 102466: My book doesn't give much help on solving this. Find the domain of f(x)3x+1/
x^2+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%283x%2B1%29%2F%28x%5E2%2B4%29 Start with the given function


x%5E2%2B4=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.

x%5E2=-4 Subtract 4 from both sides

x=0%2B-sqrt%28-4%29 Take the square root of both sides

Since you cannot take the square root of a negative number and get a real number, the result will be imaginary


So that means there are no real numbers which will make the denominator equal to zero


So the domain is:

x is the element of all real numbers