Question

Diketahui f (x) = 1/2x -1 dan (gof)(x) = 1/2x + 1. nilai g(-1)+g(0)+g(1)+g(2)+...+g(98)=​

Answer 1

Diketahui:

f(x) = 1/2x-1

(gof)(x) = 1/2x+1

Ditanyakan:

g(-1)+g(0)+g(1)+g(2)+...+g(98)

Jawab:

(gof)(x) = g(f(x))

1/2x + 1 = g(1/2x -1)

misal 1/2x - 1 = a

maka,

1/2x -1 = a

1/2x = a+2

1 = 2ax+4x

1 = x(2a+4)

1/(2a+4) = x

g(a) = 1/2(1/(2a+4)) + 1

= 1/(2/(2a+4)) + 1

= 1/(1/(a+2)) + 1

= 1. (a+2)/1 + 1

= a+3

g(x) = x+3

g(-1) = -1+3 = 2

g(0) = 0+3 = 3

maka,

a = 2

b = 1

g(-1)+g(0)+g(1)+g(2)+...+g(98)

= u(98-2)

= u96

= a+(96-1)b

= 2+(95)1

= 97

Mapel: Matematika

Kelas: 10

Materi: Komposisi Fungsi