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## One-to one functionA function f: A → B is said to be one-to one function iff ( a _{ 1} ) = f (a _{ 2} ) ⇒ ( a _{ 1} ) = ( a _{ 2} ), ( a _{ 1} )( a _{ 2} ) ∈ A Let A = {( a _{ 1} )( a _{ 2} )( a _{ 3} )( a _{ 4} )}
and B = {( b _{ 1} )( b _{ 2} )( b _{ 3} )( b _{ 4} )} Example : – Determine if the function given below is one to one. 1) To each state of India assign its Capital Solution: This is not one to one function because each state of India has different capital. 2) Function = {(2,4),(3,6),(-1,-7)} Solution : The above function is one to one because each value of range has different value of domain.3) f(x) = |x| Solution : Here to check whether the given function is one to one or not, we will consider some values of x (domain) and from the given function find the value of range(y).
Q.1 State which of the following graph shows one to one function and why?
Note : For checking 1-to-1 function on the graph, we will use a horizontal test. |
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