Student Number:_{------}
No._{----} Marks _{----}

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

(i) Show that f is one to one on (-¥, 1)È(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¢ Î (-¥,1)È(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)È(1,¥).

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

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

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On 6 Apr 2001, 12:37.