Question

1.diketahui f(x)=2x+5 dan g(x)= - 2x/x+4,maka (g^-1of^-1)(x) adalah​

2.diketahui f(3x-7) =6x-20, maka (f^-1) (x+2) =

Answer 1

Penjelasan dengan langkah-langkah:

1] (g^-1 o f^-1) (x) = (fog)^-1 (x)

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

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

(fog) (x) = 2 ((-2x)/(x + 4)) + 5

(fog) (x) = (-4x + 5 (x + 4))/(x + 4)

(fog) (x) = (-4x + 5x + 20)/(x + 4)

(fog) (x) = (x + 20)/(x + 4)

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

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

(fog) (x) = (x + 20)/(x + 4)

(fog)^-1 (x) = (-4x + 20)/(x - 1)

(g^-1 o f^-1) (x) = (-4x + 20)/(x - 1)

2] f(3x - 7) = 6x - 20

f(3x - 7) = 2 (3x - 7) - 6

f(x) = 2x - 6

y = 2x - 6

2x = y + 6

x = (y + 6)/2

f^-1 (x) = (x + 6)/2

f^-1 (x + 2) = (x + 2 + 6)/2

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

Kelas 11

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