Question

jawablah dengan benar​

Answer 1

a. F(x) = x - 5

F^-1 (x) = F(x) + 5

= x + 5

b. g(x) = 1 / (x + 5)

g^-1 (x) = 1 / g(x) - 5

= 1 / x - 5

c. (fog)(x) = f(g(x))

= f(1 / (x + 5))

= 1 / (1 / (x + 5)) - 5

= x + 5 - 5

= x

Maka (fog)^-1 (3) = 3.

d. (gof)(x) = g(f(x))

= g(x - 5)

= 1 / (x - 5 + 5)

= 1 / x

Maka, (gof)^-1 (2) = 1 / 2 = 0.5.

e. (fof)(x) = f(f(x))

= f(x - 5)

= x - 5 - 5

= x - 10

Maka (fof)^-1 (8) = 8 + 10 = 18.

f. Ketahui bahwa (g^-1 o g)(x) = x, yaitu fungsi identitas.

Jadi, (g^-1 o g)(-10) = -10.

g. Ketahui bahwa g(x) = 1/(x + 5) dan F^-1(x) = x + 5. Maka,

(F^-1 o g)(x) = F^-1(g(x)) = F^-1(1/(x + 5)) = x + 5.

Jadi, (F^-1 o g)(3) = (x + 5)(3) = 3 + 5 = 8.

Mohon maaf jika terdapat kesalahan.