Question

tolong bantu ya kak mau dikumpulin​

Answer 1

FUNGSI INVERS

Misalkan f(x) = 3x - 1, x > 0 dan g(x) = 6/5x , x > 0. Tentukan nilai x, jika (g^-1 o f^-1)(x) = 9/10

f(x) = 3x - 1

y = 3x - 1

3x = y + 1

x = (y + 1) / 3

f⁻¹(x) = (x + 1) / 3

g(x) = 6/5x

y = 6/5x

x = 6/5y

g⁻¹(x) = 6/5x

(g⁻¹ o f⁻¹)(x) = g⁻¹(f⁻¹(x))

= g((x + 1) / 3)

= 6/5((x + 1) / 3)

= 18/5(x + 1)

=18/(5x + 5)

18/(5x + 5) = 9/10

180 = 45x + 45

45x = 135

x = 3 ✔