In general, let us denote the identity function for a set C by i C . That is, define i C : C → C to be the function given by the rule i C ( x ) = x for all x ∈ C . Given that f : A → B , we say that a function g : B → A is a left inverse for f if g ∘ f = i A ; and we say that h : B → A right inverse for f if f ∘ h = i B . Give an example of a function that has a right inverse but no left inverse.
In general, let us denote the identity function for a set C by i C . That is, define i C : C → C to be the function given by the rule i C ( x ) = x for all x ∈ C . Given that f : A → B , we say that a function g : B → A is a left inverse for f if g ∘ f = i A ; and we say that h : B → A right inverse for f if f ∘ h = i B . Give an example of a function that has a right inverse but no left inverse.
Solution Summary: The author explains that a function f:Ato B is said to be injective if for each pair of distinct points of A, their images under
In general, let us denote the identity function for a set
C
by
i
C
. That is, define
i
C
:
C
→
C
to be the function given by the rule
i
C
(
x
)
=
x
for all
x
∈
C
. Given that
f
:
A
→
B
, we say that a function
g
:
B
→
A
is a left inverse for
f
if
g
∘
f
=
i
A
; and we say that
h
:
B
→
A
right inversefor
f
if
f
∘
h
=
i
B
.
Give an example of a function that has a right inverse but no left inverse.
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