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Byju's Answer
Standard XII
Mathematics
Many-One into Function
Let fx =11- x...
Question
Let
f
x
=
1
1
-
x
.
Then
,
f
o
f
o
f
x
(a)
x
for
all
x
∈
R
(b)
x
for
all
x
∈
R
-
1
(c)
x
for
all
x
∈
R
-
0
,
1
(d) none of these
Open in App
Solution
Domain of
f
:
1
-
x
≠
0
⇒
x
≠
1
Domain of
f
=
R
-
1
Range of
f
:
y
=
1
1
-
x
⇒
1
-
x
=
1
y
⇒
x
=
1
-
1
y
⇒
x
=
y
-
1
y
⇒
y
≠
0
Range of
f
=
R
-
0
So,
f
:
R
-
1
→
R
-
0
and
f
:
R
-
1
→
R
-
0
Range of
f
is not a subset of the domain of
f
.
Domain
f
o
f
=
x
:
x
∈
domain of
f
and
f
x
∈
domain of
f
Domain
f
o
f
=
x
:
x
∈
R
-
1
and
1
1
-
x
∈
R
-
1
Domain
f
o
f
=
x
:
x
≠
1
and
1
1
-
x
≠
1
Domain
f
o
f
=
x
:
x
≠
1
and
1
-
x
≠
1
Domain
f
o
f
=
x
:
x
≠
1
and
x
≠
0
Domain
f
o
f
=
R
-
0
,
1
f
o
f
x
=
f
f
x
=
f
1
1
-
x
=
1
1
-
1
1
-
x
=
1
-
x
1
-
x
-
1
=
1
-
x
-
x
=
x
-
1
x
For range of
f
o
f
,
x
≠
0
Now,
f
o
f
:
R
-
0
,
1
→
R
-
0
and
f
:
R
-
1
→
R
-
0
Range of
f
o
f
is not a subset of domain of
f
.
Domain
f o
f
o
f
=
x
:
x
∈
domain of
f
o
f
and
f
o
f
x
∈
domain of
f
Domain
f o
f
o
f
=
x
:
x
∈
R
-
0
,
1
and
x
-
1
x
∈
R
-
1
Domain
f o
f
o
f
=
x
:
x
≠
0
,
1
and
x
-
1
x
≠
1
Domain
f o
f
o
f
=
x
:
x
≠
0
,
1
and
x
-1
≠
x
Domain
f o
f
o
f
=
x
:
x
≠
0
,
1
and
x
∈
R
Domain
f o
f
o
f
=
R
-
0
,
1
f
o
f
o
f
x
=
f
f
o
f
x
=
f
x
-
1
x
=
1
1
-
x
-
1
x
=
x
x
-
x
+
1
=
x
So,
f
o
f
o
f
x
=
x
,
where
x
≠
0
,
1
So, the answer is (c).
Suggest Corrections
0
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Let
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(b) f (x) is continuous for all for all × in its domain but not differentiable at x = ± 1
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Q.
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x
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