In 44-55 indicate which of the function in the referenced exercise are one-to-one correspondences. For each function that is a one-to-one correspondence, find the inverse function. Exercise 12b
Whether the given function is one-to-one correspondence and also find the inverse of the given function if it exists.
is defined by the rule for all real numbers .
One-to-one function: The distinct elements in domain are mapped with distinct elements in co-domain.
Onto function: Every element in co-domain must be mapped with the element in domain.
Before find its inverse first prove that is both one-to-one and onto.
To prove is one-to-one.
Let and be any two elements of
By definition of
Subtracting to both sides,
Divided by from both side, gives:
Hence, is one-to-one.
To proof is onto