SOLUTION: I'm not sure if I am posting this in the right area. But I need to: For the indicated functions f and g, find the functions f+g,f-g,fg, and f/g and find their domains. f(x)=3x

Algebra ->  Exponents -> SOLUTION: I'm not sure if I am posting this in the right area. But I need to: For the indicated functions f and g, find the functions f+g,f-g,fg, and f/g and find their domains. f(x)=3x       Log On


   

Question 30449: I'm not sure if I am posting this in the right area. But I need to:
For the indicated functions f and g, find the functions f+g,f-g,fg, and f/g and find their domains.
f(x)=3x g(x)=x^2+4
Could you show me how this is done. I did it using word and cannot paste the answer in here and need something to check my work by.
Thank you so much!
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
As to the domains, you need to know the domains of the originals to base them upon. You haven't supplied this info, so i assume both f(x) and g(x) have domains of "any real value".

f+g --> +3x+%2B+x%5E2+%2B+4+
f+g --> +x%5E2+%2B+3x+%2B+4+ and its domain is also "any real value of x" since we CAN put in any value we like and get a valid y-value out.

f-g --> +3x+-+%28x%5E2+%2B+4%29+
f-g --> +3x+-+x%5E2+-+4%29+
f-g --> +-x%5E2+%2B+3x+-+4%29+ and its domain is also "any real value of x" since we CAN put in any value we like and get a valid y-value out.

fg --> +f%28x%5E2+%2B+4%29+
fg --> +%283x%29%5E2+%2B+4+
fg --> +9x%5E2+%2B+4+ and its domain is also "any real value of x" since we CAN put in any value we like and get a valid y-value out.

By f/g, i assume you mean...
f/g --> +%283x%29%2F%28x%5E2%2B4%29+ in which case the domain is again "any real value of x". If you have done Complex Numbers, there are 2 complex numbers that are NOT allowed, since we are trying to avoid the denominator being zero, because when that happens, the fraction zooms off to infinity, which is a bad thing mathematically.

jon.