Question 30449
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 + x^2 + 4 }}}
f+g --> {{{ x^2 + 3x + 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 - (x^2 + 4) }}}
f-g --> {{{ 3x - x^2 - 4) }}}
f-g --> {{{ -x^2 + 3x - 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.


fg --> {{{ f(x^2 + 4) }}}
fg --> {{{ (3x)^2 + 4 }}}
fg --> {{{ 9x^2 + 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 --> {{{ (3x)/(x^2+4) }}} 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.