Penjelasan dengan langkah-langkah:

1. g(f(x)) = 2(2x² + 4x -1) + 8

= 4x² + 8x - 2 + 8

g(f(x)) = 4x² + 8x + 6

g(f(2)) = 4(2)² + 8(2) + 6 = 4(4) + 16 + 6 = 38

2. f(x) = x - 12

f(g(x)) = 2x² + 8x + 7

f(g(x)) = g(x) - 12 = 2x² + 8x + 7

g(x) = 2x² + 8x + 7 + 12

g(x) = 2x² + 8x + 19

3. f(x) = x - 3

g(f(x)) = x² + 4x - 1

g(x-3) = x² + 4x - 1

untuk mencari g(x) maka kita harus cari invers dari x-3 yaitu x+3 lalu di substitusi ke x

g(x) = (x+3)² + 4(x+3) - 1

g(x) = x²+6x+9+4x+12-1

g(x) = x²+10x+20

g(x+1) = (x+1)² + 10(x+1) + 20

g(x+1) = x² + 2x + 1 + 10x + 10 + 20

g(x+1) = x² + 12x + 31

4.

h(x) = (x+8)/(2x-1)

(h(x))(2x-1) = x+8

2(h(x))x - h(x) = x + 8

2(h(x))x-x = 8+h(x)

x(2h(x)-1) = 8 + h(x)

x = (8+h(x))/(2h(x)-1)

karna diinverse maka kita balik x jadi h^-1 (x) sedangkan h(x) jadi x

h^-1(x) = (8+x)/(2x-1)

h^-1(2) = (8+2)/(2(2)-1) = 10/3

5. h^(-1)(x) = (x+3)/(x-1)

g(x) = 2x+8

g^(-1)(x) = (x-8)/2

h^(-1)(g^(-1)(x)) = (((x-8)/2)+3)/(((x-8)/2)-1)

h^(-1)(g^(-1)(x)) = (((x-8)/2)+(6/2))/(((x-8)/2)-2/2)

h^(-1)(g^(-1)(x)) = ((x-8+6)/2)/((x-8-2)/2)

h^(-1)(g^(-1)(x)) = ((x-2)/2)/((x-10)/2)

h^(-1)(g^(-1)(x)) = ((x-2)/2)×(2/(x-10))

h^(-1)(g^(-1)(x)) = (x-2)/(x-10)