First find f g f g fg and fg Then determine the domain for

First find f + g, f - g, fg and f/g. Then determine the domain for each function. f(x) = 7x + 6/x^2 - 9, g(x) = 6x + 3/x^2 - 9 (f + g)(x) =

Solution

f(x) = ( 7x +6)/(x^2 - 9) ; g(x) = (6x +3)/(x^2 - 9)

f+g = f(x) + g(x) = ( 7x +6+ 6x +3)/( x^2 -9) = ( 13x + 9)/(x^2 - 9)

f - g = f(x) - g(x) = ( 7x +6 - 6x -3)/( x^2 -9) = ( x +3)/(x^2 -9)

f*g = f(x)*g(x) = ( 7x +6)/(x^2 - 9) (6x +3)/(x^2 - 9) = ( 7x +6)/( x^2 -9)^2

f/g = f(x)/g(x) = (7x +6)/(6x +3)