SOLUTION: hi what would the domain of 5x/x^3+36x be i've tried to find what number would give me 36 but i don't know if that's the right method

Algebra ->  Functions -> SOLUTION: hi what would the domain of 5x/x^3+36x be i've tried to find what number would give me 36 but i don't know if that's the right method      Log On


   

Question 559661: hi what would the domain of 5x/x^3+36x be i've tried to find what number would give me 36 but i don't know if that's the right method
Answer by KMST(5347) About Me  (Show Source):
You can put this solution on YOUR website!
The domain of f(x) = 5x/(x^3+36x) = 5x%2F%28x%5E3%2B36x%29
includes all real numbers except those that make x%5E3%2B36x=0
Factoring, we get:
x%5E3%2B36x=0 ==> x%28x%5E2%2B36%29=0
In the real numbers there are no solutions for
x%5E2%2B36=0, so the only solution would be x=0.
For x=0, the function does not exist; it's undefined.
For any other value of x, we can simplify to
f(x) = 5x%2F%28x%28x%5E2%2B36%29%29 = 5cross%28x%29%2F%28cross%28x%29%28x%5E2%2B36%29%29 = 5%2F%28x%5E2%2B36%29
The graph of the function is the same as the graph of
f(x) = 5%2F%28x%5E2%2B36%29 , except that it does not exist for x=0.
There is a hole where (0,5/36) would be.
The number x=0 is the only real number excluded from the domain of the function.