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Jawaban:

No. 1

f(x) = 12x + 6

Misalkan a = 12 dan b = 6, maka

f^-1(x) = (x – b) /a

= (x – 6) /12

No. 2

f(x) = (6x + 2) / (-2x – 7)

Misalkan a = 6, b = 2, c = -2, dan d = -7

Maka

f^-1(x) = (-dx + b) / (cx – a)

= (-(-7)x + 2) / (-2x – 6)

= (7x + 2) / (-2x – 6)

No. 3

f(x) = 1/2 x – 1

g(x) = 2x + 4

(g o f)(x) = g(f(x))

= 2(1/2 x – 1) + 4

= x – 1/2 + 4

= x + 7/2

Misalkan a = 1 dan b = 7/2, maka

(g o f)^-1(x) = (x – b) /a

= (x – 7/2) / 1

= x – 7/2

(g o f)^-1(10) = 10 – 7/2 = 13/2

No. 4

f(x) = 1/x

g(x) = 2x – 1

(g o f)(x) = 2(1/x) – 1

= 2/x – 1

= (2 – x) /x

Misalkan a = -1, b = 2, c = 1, d = 0

Maka

(g o f)^-1(x) = (-dx + b) / (cx – a)

= (0 + 2) / (x – (-1))

= 2 / (x + 1)

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