Question

Bantu donk bray, lagi niat nih

Answer 1

G(x)= (x +1)/(x - 1)
g⁻¹(x) = (-x -1)/(-x+1) = (x + 1)/(x -1)

fog(x) = 1/ ( x+1)
f(x) = (fog) o g⁻¹ (x)
f(x) = 1/ {(x+1)/(x-1) +1)}  ...kalikan (x-1)/(x-1)
f(x) = (x-1)/((x+1)+(x-1)}
f(x) = (x-1)/(2x)
f(x) = 1/2 ( x/x - 1/x)
f(x) = 1/2 ( 1 - 1/x)

17.
Lim (x->1) f(x) = 3

lim (x-1) g(x) = lim(x->3) (x + √x -2)/ (x - 1)
= lim(x->1) (√x +2)(√x - 1) / ( √x -1)(√x + 1)
= lim(x->1) (√x  +2) /(√x +1)
x = 1 --> lim (x->1) g(x)= 3/2

lim (x->1) f(x). g(x) = 3 (3/2) = 9/2