If fx 3x 3 and gx x2 3x 4 then find f g x f g x f mid

If f(x) = 3x + 3 and g(x) = x^2 - 3x - 4, then find: (f + g) (x) (f - g) (x) (f middot g) (x) (f/g) (x) (f g) (x) (g f) (x) f^-1 (x)

Solution

given f(x)=3x +3 ,g(x)=x²-3x -4

a)(f+g)(x)=f(x)+g(x)

=3x +3 +x²-3x -4

=x² -1

b)(f-g)(x)=f(x)-g(x)

=3x +3 -x²+3x +4

=-x² +6x+7

c)(f.g)(x)=f(x).g(x)

=(3x +3)(x²-3x -4)

=3x³-9x² -12x +3x²-9x -12

=3x³-6x² -21x -12

d)

(f/g)(x)=f(x)/g(x)

=(3x +3)/(x²-3x -4)

=3(x+1)/((x-4)(x+1))

=3/(x-4)

e)(fog)(x)

=f(g(x))

=3(x²-3x -4)+3

=3x²-9x -12+3

=3x²-9x -9

f)(gof)(x)

=g(f(x))

=(3x+3)²-3(3x+3) -4

=9x²+18x+9-9x-9+4

=9x²+9x+4

g)let f(x)=y

=>x=f^-1(y)

3x+3=y

x=(y-3)/3

f^-1(y)=(y-3)/3

f^-1(x)=(x-3)/3