Show that the function
(i) is one – one into.
(ii) is many – one into

Solution:

(i)

is one – one into.
As the function is monotonically increasing from the domain
is one -one
Range of (codomain)
is into
is one one into.

(ii)

is many – one into

The lines cut the curve in 2 equal valued points of , therefore, the function is many one.
Range of (codomain)
is into
is many – one into