Let fx 7x 5 and gx 2x 7 Find f g xfgx fgx f0 gx and g0

Let f(x) = 7x + 5 and g(x) = 2x - 7. Find (f + g) (x).(f_g)(x), (f/g)(x) (f_0 g)(x) and (g_0 f) (x). Give the domain of each (f + g) (x) =

solution-

f(x)=7x+5

g(x)=2x-7

now

(f+g)(x)=(7x+5)+(2x-7)(x)= 9x-2(x) ; domain all real values

(f-g)(x)=(7x+5)-(2x-7)(x)= 5x+12(x) ; domain all real values

(f*g)(x)=(7x+5)*(2x-7)(x)= 14x²-39x-35(x); domain all real values

(f/g)(x)=[(7x+5)/(2x-7)](x) ; domain all real values but except x= 7/2

(fog)(x)=7(2x-7)+5=14x-44;domain all real values

(gof)(x)=2(7x+5)-7=14x+3;domain all real values