Question

Let f(x) = ax/(x+1), x ≠ -1.Then write the value of a satisfying f(x)) = x for all x ≠ - 1.

Answer 1

f(x) = ax/(x+1), x ≠ -1

a²x = ax²+x²+x 

x²(a+1)+x(1- a²) = 0 

x² (a+1)+x(1-a)(1+a) = 0 

(a+1)(x²+x(1-a)) = 0 

a+1 = 0 

Therefore, 

a = -1