Diketahui f(x) = 5x + 2/4x – 1, x tidak sama dengan 1/4. Tentukan: a. f^-1(-1) b. f^-1(2) c. x jika f^-1(x) = -3 d. x jika f^-1(x) = 5/7 Jawab:​

Penjelasan dengan langkah-langkah:

f(x) = (5x + 2)/(4x – 1)

(4x)f(x) – f(x) = 5x + 2

(4x)f(x) – 5x = f(x) + 2

x (4f(x) – 5) = f(x) + 2

x = {f(x) + 2} / {4f(x) – 5}

f^-1 (x) = (x + 2)/(4x – 5) ; x # 5/4

# = tidak sama dengan

a. f^-1 (-1) = (-1 + 2)/(4(-1) – 5)

= 1/(-4 – 5) = 1/(-9) = -1/9

b. f^-1 (2) = (2 + 2)/(4(2) – 5)

= 4/(8 – 5) = 4/3 = 1 ⅓

c. -3 = (x + 2)/(4x – 5)

-3(4x – 5) = x + 2

-12x + 15 = x + 2

-12x – x = 2 – 15

-13x = -13

x = 1

d. 5/7 = (x + 2)/(4x – 5)

5(4x – 5) = 7(x + 2)

20x – 25 = 7x + 14

20x – 7x = 25 + 14

13x = 39

x = 39/13

x = 3