Let R0 be the set of all nonzero real numbers. Then, show that the function is one-one and onto.
To prove: function is one-one and onto
We have,
For, f(x1) = f(x2)
⇒ x1 = x2
When, f(x1) = f(x2) then x1 = x2
∴ f(x) is one-one
Let f(x) = y such that
Since ,
⇒ x will also , which means that every value of y is associated with some x
∴ f(x) is onto
Hence Proved