Answer to Question #125095 in Algebra for Ojugbele Daniel

Question

Show that f:x mapping x/x+1 is one to one mapping

Answer 1

f(x) = x/(x+1)

For one to one mapping

we prove f(x₁)=f(x₂) $\to$ x₁=x₂ .

Let

f(x₁) = x₁/(x₁+1)

f(x₂)= x₂/(x₂+1)

now

f(x₁)=f(x₂)

x₁/(x₁+1) = x₂/(x₂+1)

x₁(x₂+1) = x₂(x₁+1)

x₁x₂+x₁ = x₂x₁+x₂

x₁ = x₂

hence it was proved that this function is one to one mapping.