Write the inverse of the given function.
Problem 1 :
{ (1, 5) (2, 7) (3, -2) (4, -3) }
Problem 2 :
{ (0, 6) (4, 2) (-1, 7) (-2, 8) }
Problem 3 :
{ (1, 1) (2, 2) (3, 3) (4, 4) }
Problem 4 :
{ (1, k) (2, k+1) (3, k+2) }
Problem 5 :
Let f = {(3, -2) (4, -) (5, -1)
a) Write the function formed by interchanging x and y-coordinate.
b) Is this new relation a function? If not explain why?
State true or false :
Problem 6 :
The relation formed by interchanging x and y in each pair of the function is also a function.
Problem 7 :
The relation formed by interchanging x and y in each pair of a one to one function is also one to one function.
Problem 8 :
What is the inverse of the function
{ (3, 1) (4, -1) (-2, 6)} ?
1) { (3, -1) (4, 1) (-2, -6) }
2) { (-1, 3) (1, 4) (-6, -2) }
3) { (-3, -1) (-4, 1) (2, -6) }
4) { (1, 3) (-1, 4) (6, -2) }
1) { (5, 1) (7, 2) (-2, 3) (-3, 4) }
2) { (6, 0) (2, 4) (7, -1) (8, -2) }
3) { (1, 1) (2, 2) (3, 3) (4, 4) }
4) { (k, 1) (k+1, 2) (k + 2, 3) }
5) a) f^{-1} = {(-2, 3) (-2, 4) (-1,5)
b) It is not a function, because one of the inputs is associated with more than one output.
That is,
-2 is associated with 3 and -2 is associated with 4. So, it is no t a function.
6) False
7) True.
Because if the original function is one to one, each element will have different output. So, it's inverse function will also be one to one function.
8) f^{-1} = { (1, 3) (-1, 4) (6, -2)}
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM