GMAT GRE 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th grade math 8th grade math 9th grade math 10th grade math 11th grade math 12th grade math Precalculus Worksheets Chapter wise Test MCQ's Math Dictionary Graph Dictionary Multiplicative tables Math Teasers NTSE Chinese Numbers CBSE Sample Papers |
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). How to determine one-to one function from the graph?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.Horizontal test : Draw a horizontal line on the graph, if that line cuts the graph in two points then the given graph is not 1-to-1 graph. Solution : In the 1st graph if we draw a horizontal line then that line cuts the graph at one point only so the 1st graph is 1-to-1 function graph. In the 2nd graph if we draw a horizontal line then that line cuts the graph at one point only so the 2nd graph is 1-to-1 function graph. In the 3rd graph if we draw a horizontal line then that line cuts the graph at two points so the 3rd graph is not 1-to-1 function graph. Q.2 Show that the given function (x+2)/(x-3) = (y+2)/(y-3) is one-to one function. Solution : (x+2)/(x-3) = (y+2)/(y-3) (x+2 )(y-3) = (y+2)(x-3) ----(cross multiply) ⇒ xy -3x + 2y - 6 = xy -3y + 2x - 6 ⇒ -3x + 2y = -3y + 2x -----( xy and -6 get cancelled out) ⇒ -3x -2x = -3y - 2y ----( bring the like terms together) ⇒ -5x = -5y ⇒ x = y ----( divide both side by negative 5) So the given function is one-to one function. From one to one function to Home
More To Explore
|
||||||||||