Quiz 4 Quiz 4                              Friday, April 6, 2001



NAME:

Student Number:------            No.----           Marks ----






(25 Marks)    Let f(x) = [(x+1)/(x-1)], x 1.

(i) Show that f is one to one on (-, 1)(1,).

(ii) Find the domain of the inverse function of f.

(iii) Find a formula for the inverse function.

Solution (i) Proof. Assume that f(x) = f(x), x,x (-,1)(1,). Then [(x+1)/(x-1)] = [(x+1)/(x-1)]. This implies 1+[2/(x-1)] = 1+[2/(x-1)] and x = x. Hence, f is one to one on (-, 1)(1,).

(ii) Let y = [(x+1)/(x-1)]. Then x = [(1+y)/(y-1)]. Hence, the domain of the inverse function is (-,1)(1,).

(iii) f-1(x) = [(1+x)/(x-1)], x 1.


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On 6 Apr 2001, 12:37.