Question

Diketahui
f(x) =x+1/x-1
g(x) = 3x+3/x-1
tentukan
(f o g) (x) =
(g o f) (x) =

Answer 1

Diketahui
f(x) =x+1/x-1
g(x) = 3x+3/x-1
tentukan
(f o g) (x) =
f(g(x)) = (3x+3/x-1) + 1 / (3x+3/x-1)-1
=[3x+3+x-1 /x-1 ] / [3x+3-(x-1)/ x-1)
= 4x+2/x-1 kali x-1/2x+4
= 4x+2 / 2x+4
= 2(2x+1) / 2(x+2)
=2x+1/x+2

(g o f) (x) =

3[(x+1) /(x-1)] + 3 / [x+1/x-1) -1]
= 3x+3/x-1 + 3 /[x+1-(x-1) /(x-1)
=[3x+3+3(x-1) / x -1] / 2/x-1
= [6x / x -1 kali x-1 / 2)
= 6x / 2
= 3x