Q5 of 107 Page 18

State with reason whether following functions have inverse

g : {5, 6, 7, 8} → {1, 2, 3, 4} with


g = {(5, 4), (6, 3), (7, 4), (8, 2)}

It is given that g : {5, 6, 7, 8} → {1, 2, 3, 4} with

g = {(5, 4), (6, 3), (7, 4), (8, 2)}


From the given definition of,


We can see that f is a many one function as:


g(5) = g(7) = 4


= > g is not one- one.


Therefore, function g does not have an inverse.


More from this chapter

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4

If , show that fof(x) = x, for all . What is the inverse of f?

5

State with reason whether following functions have inverse

f : {1, 2, 3, 4} → {10} with


f = {(1, 10), (2, 10), (3, 10), (4, 10)}

 5

State with reason whether following functions have inverse

h: {2, 3, 4, 5} → {7, 9, 11, 13} with


h = {(2, 7), (3, 9), (4, 11), (5, 13)}

 6

Show that f : [–1, 1] → R, given by is one-one. Find the inverse of the function f : [–1, 1] → Range f.

(Hint: For y ∈ Range f, y = , for some x in [–1, 1], i.e., )