SOLUTION: I need the domain of the following problem: {{{g(x)=5x/x^2+25}}} Please. College Algebra. If I can figure out the meaning of domain and see it being worked in a problem, I should

Algebra ->  Functions -> SOLUTION: I need the domain of the following problem: {{{g(x)=5x/x^2+25}}} Please. College Algebra. If I can figure out the meaning of domain and see it being worked in a problem, I should       Log On


   

Question 151704: I need the domain of the following problem: g%28x%29=5x%2Fx%5E2%2B25
Please. College Algebra. If I can figure out the meaning of domain and see it being worked in a problem, I should be able to work it.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%285x%29%2F%28x%5E2%2B25%29 Start with the given function


x%5E2%2B25=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=-25 Subtract 25 from both sides.


x=sqrt%28-25%29 Take the square root of both sides.


x=sqrt%28-1%29%2Asqrt%2825%29 Factor sqrt%28-25%29 into sqrt%28-1%29%2Asqrt%2825%29


x=i%2Asqrt%2825%29 Replace sqrt%28-1%29 with "i"


x=5%2Ai or x=-5i Take the square root of 25 to get 5 or -5


Since the values x=5%2Ai or x=-5i make the denominator zero, this means that there are no real x values that make the denominator zero (since 5i and -5i are both complex).


So you can plug in any real number for x and you'll get a result for f(x).



If that doesn't make any sense to you, then try to think of it like this:

x%5E2 is always positive. So there are no real values that make x%5E2=-25 true. That's why the domain includes all real numbers.



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Answer:

So the domain of the function in set-builder notation is:





In plain English, this reads: x is the set of all real numbers (In other words, x can be any number)


Also, in interval notation, the domain is: