Diketahui bahwa :

— f(x) = 2x - 3

Ditanya :

• fog (3)
• gof (-2)
• f^-1 (5)
• g^-1 (4)

Penyelesaian :

• fog (3)

fog (x) = f(g(x))

fog (x) = f(x-2/4x+1)

fog (x) = 2(x-2/4x+1) - 3

fog (3) = 2(3-2/4(3)+1) + 3

fog (3) = 2(1/13) + 3

fog (3) = 2/13 + 39/13

fog (3) = 41/13

fog (3) = 3 2/13

• gof (-2)

gof (x) = g(f(x))

gof (x) = g(2x - 3)

gof (x) = (((2x - 3)-2)/(4(2x-3) +1)l + 3

gof (x)= ((2x - 5)/(8x -11)) + 3

gof (-2) = ((-4 - 5)/(-16 - 11)) + 3

gof (-2) = (-9/-27) + 3

gof (-2) = 1/3 + 3

gof (-2) = 3 1/3

• f^-1 (5)

f(x) = 2x - 3

y = 2x - 3

y + 3 = 2x

(y + 3)/2 = x

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

f^-1 (5) = (5+3)/2

f^-1 (5) = 4

• g^-1 (4)

g(x) = (x - 2)/(4x - 1) --> g^-1(x) = -dx + b/cx - a

g^-1 (x) = (x - 2)/(4x - 1)

g^-1 (4) = (4-2)/(16-1)

g^-1 (4) = 2/15