SOLUTION: What is the domain of f(x)= 6x+5/x+5

Question 85127: What is the domain of f(x)= 6x+5/x+5
Found 2 solutions by jim_thompson5910, chitra:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since we cannot divide by zero, we can find exclusions in the domain by setting the denominator equal to zero and solving for x:

Set the denominator equal to zero
Solve for x

Since x=-5 makes the denominator equal to zero, we must exclude -5 from our domain. So our domain is: x is the set of all real numbers, except x cannot equal -5. Basically we can choose any number we want, except -5, and plug it in for x to get a real number output.

In interval notation, the domain would look like this:

where the "U" stands for union

Notice when we graph the equation we get

and you can see that x=-5 is not part of the domain (note: the vertical line is not part of the graph, it is an asymptote)

Answer by chitra(359) (Show Source): You can put this solution on YOUR website!
Here the given function is f(x)=

Here we observe that the given function has both the numerator and a denominator. Here we see to that plugging in any of the values for "x" does not make the entire function to zero. So to find the domain we equate the denominator to zero.

Here the domain is x + 5
==> x + 5 = 0
==> x = -5

This implies that the domain consists of all the real numbers except -5 (since plugging in x = -5 makes the entire function zero)

Hence, D = {R - (-5)}

Hence, the solution.

Regards
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