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Byju's Answer
Standard XII
Mathematics
Cartesian Product
If f(g(x)) is...
Question
If f(g(x)) is one one then which of f(x),g(x) is necessary one one? Similarly for onto?
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Similar questions
Q.
If
f
(
x
)
=
a
x
+
b
and
g
(
x
)
=
c
x
+
d
such that
f
(
g
(
x
)
)
=
g
(
f
(
x
)
)
,
then which one of the following is correct?
Q.
Which of the following statements are incorrect?
I If
f
(
x
)
and
g
(
x
)
are one to one then
f
(
x
)
+
g
(
x
)
II If
f
(
x
)
and
g
(
x
)
are one to one then
f
(
x
)
.
g
(
x
)
III If
f
(
x
)
is odd then it is necessarily one to one.
Q.
Let
f
:
R
→
R
be defined as
f
(
x
)
=
2
x
–
1
and
g
:
R
–
{
1
}
→
R
be defined as
g
(
x
)
=
x
−
1
2
x
−
1
. Then the composition function
f
(
g
(
x
)
)
is:
Q.
Which of following statements is/are INCORRECT?
I. If
f
(
x
)
and
g
(
x
)
are one-one, then
f
(
x
)
+
g
(
x
)
is also one-one.
II. If
f
(
x
)
and
g
(
x
)
are one-one, then
f
(
x
)
.
g
(
x
)
is also one-one.
III. If
f
(
x
)
is odd, then it is necessarily one to one.
Q.
Let f : R
→
R be a function. Define g:R
→
by g(x) = |f(x)| for all x. Then g is
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