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Byju's Answer
Standard XII
Mathematics
Continuity in an Interval
Draw the grap...
Question
Draw the graph of the function
f
:
R
→
R
defined by
f
(
x
)
=
x
3
,
x
ϵ
R
.
Open in App
Solution
Drawing diagram of function
f
(
x
)
=
x
3
,
x
ϵ
R
f
(
x
)
=
x
3
,
x
ϵ
R
(given)
Put
x
=
0
,
1
,
−
1
,
2
,
−
2
we get
f
(
0
)
=
0
,
f
(
1
)
=
1
,
f
(
−
1
)
=
−
1
,
f
(
2
)
=
8
,
f
(
−
2
)
=
−
8
Suggest Corrections
15
Similar questions
Q.
Draw the graph of function
f
:
R
→
R
defined by
f
(
x
)
=
|
x
−
2
|
. Also write its domain and Range.
Q.
Classify the following functions as injection, surjection or bijection :
(i) f : N → N given by f(x) = x
2
(ii) f : Z → Z given by f(x) = x
2
(iii) f : N → N given by f(x) = x
3
(iv) f : Z → Z given by f(x) = x
3
(v) f : R → R, defined by f(x) = |x|
(vi) f : Z → Z, defined by f(x) = x
2
+ x
(vii) f : Z → Z, defined by f(x) = x − 5
(viii) f : R → R, defined by f(x) = sinx
(ix) f : R → R, defined by f(x) = x
3
+ 1
(x) f : R → R, defined by f(x) = x
3
− x
(xi) f : R → R, defined by f(x) = sin
2
x + cos
2
x
(xii) f : Q − {3} → Q, defined by
f
x
=
2
x
+
3
x
-
3
(xiii) f : Q → Q, defined by f(x) = x
3
+ 1
(xiv) f : R → R, defined by f(x) = 5x
3
+ 4
(xv) f : R → R, defined by f(x) = 3 − 4x
(xvi) f : R → R, defined by f(x) = 1 + x
2
(xvii) f : R → R, defined by f(x) =
x
x
2
+
1
[NCERT EXEMPLAR]
Q.
Let
f: R
→
R
be function defined by f(x) =
x
3
+ 4.
Then f
is
Q.
Show that the function
f
:
R
→
{
x
ϵ
R
:
−
1
<
x
<
1
}
defined by
f
(
x
)
=
x
1
+
|
x
|
x
ϵ
R
is one one and onto function.
Q.
Find whether the following functions are one-one , onto or not :
f
:
R
→
R
defined by
f
(
x
)
=
x
2
+
3
for all
x
ϵ
R
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Continuity in an Interval
Standard XII Mathematics
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