Question

Show that the function f : R → {x ∈ R : -1 < x < 1} defined by f(x) = x/(1 + |x|), x ∈ R is one-one and onto function. Hence find f^-1(x). 

Answer 1

Here, f : R → {x ∈ R : -1 < x < 1} is defined by f(x) = x/(1 + |x|), x ∈ R

So, f is onto function. 

Clearly,