7a) (fog)^(-1)(x)=(6-x)/10

(gof)^(-1)(x)=(-x+3)/10

7b) (fog)^(-1)(x)=(x-2)/3x, x≠0

(gof)^(-1)=(3x-18)/(x-4), x≠4

7c) (fog)^(-1)(x)=(-3x+6)/(-10x-6), x≠-6/10

(gof)^(-1)(x)=(-6x-15)/(4x-3), x≠3/4

Penjelasan dengan langkah-langkah:

fungsi komposisi dan invers

7a) f(x)=2x

g(x)=3-5x

(fog)(x)

=f(g(x))

=f(3-5x)

=2(3-5x)

=6-10x

(fog)^(-1)(x)

invers dari (fog)(x)

cara 1 dengan menggunakan permisalan

(fog)(x)=6-10x

y=6-10x

10x=6-y

x=(6-y)/10

(fog)^(-1)(x)=(6-x)/10

cara 2 dengan rumus

f(x)=ax+b

f^(-1)(x)=(x-b)/a

(fog)(x)=-10x+6

(fog)^(-1)(x)=(x-6)/-10

(fog)^(-1)(x)=(-x+6)/10

(gof)(x)

=g(f(x))

=g(2x)

=3-5(2x)

=3-10x

(gof)^(-1)(x)=(x-3)/-10

(gof)^(-1)(x)=(-x+3)/10

7b) f(x)=2/(x-3)

g(x)=4-3x

(fog)(x)

=f(g(x))

=f(4-3x)

=2/((4-3x)-3)

=2/(-3x+1)

dengan menggunakan permisalan

(fog)(x)=2/(-3x+1)

y=2/(-3x+1)

y(-3x+1)=2

-3xy+y=2

-3xy=2-y

x(-3y)=2-y

x=(2-y)/-3y

x=(y-2)/3y

(fog)^(-1)(x)=(x-2)/3x, x≠0

dengan rumus

f(x)=(ax+b)/(cx+d)

f^(-1)(x)=(-dx+b)/(cx-a)

(fog)(x)=(2/(-3x+1))

(fog)^(-1)(x)=(-x+2)/(-3x)

(fog)^(-1)(x)=(x-2)/3x, x≠0

(gof)(x)

=g(f(x))

=g(2/(x-3))

=4-3(2/(x-3))

=4-(6/(x-3))

=(4(x-3)-6)/(x-3)

=(4x-12-6)/(x-3)

=(4x-18)/(x-3)

(gof)^(-1)=(3x-18)/(x-4), x≠4

7c) f(x)=(2x+3)/(x-5)

g(x)=3/2x

(fog)(x)

=f(g(x))

=f(3/2x)

=(2(3/2x)+3)/((3/2x)-5)

=((3/x)+3)/((3/2x)-5)

=((3+3x)/x)/((3-5(2x))/2x)

=((3+3x)/x)/((3-10x)/2x)

=(2x(3+3x))/((3-10x).x)

=(2(3+3x))/(3-10x)

=(6+6x)/(3-10x)

(fog)^(-1)(x)=(-3x+6)/(-10x-6), x≠-6/10

(gof)(x)

=g(f(x))

=g((2x+3)/(x-5))

=3/(2(2x+3)/(x-5))

=3(x-5)/(2(2x+3))

=(3x-15)/(4x+6)

(gof)^(-1)(x)=(-6x-15)/(4x-3), x≠3/4

semoga dapat dipahami dan bermanfaat