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अर्कज
Subject: Maths
, asked on 6/5/18
L
e
t
f
(
x
)
=
x
2
a
n
d
g
(
x
)
=
2
x
+
1
b
e
t
w
o
r
e
a
l
f
u
n
c
t
i
o
n
s
.
F
i
n
d
(
f
+
g
)
(
x
)
,
(
f
-
g
)
(
x
)
,
(
f
g
)
(
x
)
,
f
g
(
x
)
Answer
1
अर्कज
Subject: Maths
, asked on 6/5/18
Example 15:
Example 15: Define the real valued function
f
:
R
-
o
→
R
defined
by
f
x
=
1
x
,
x
∈
R
-
0
. Complete the Table given below using this definition. What is the domain and range of this function ?
x
-2
-1.5
-1
-0.5
0.25
0.5
1
1.5
2
y
=
1
x
...
...
...
...
...
...
...
...
...
Answer
2
अर्कज
Subject: Maths
, asked on 6/5/18
Example 14
Answer
1
Eshita Rastogi
Subject: Maths
, asked on 6/5/18
Let
f
: R
+
→ R, where R
+
is the set of all positive real numbers, be such that
f
(
x
) = log
e
x
.
Determine
(i) the image set of the domain of
f
(ii) {
x
:
f
(
x
) = – 2}
(iii) whether
f
(
xy
) =
f
(
x
) +
f
(
y
) holds.
Answer
1
Eshita Rastogi
Subject: Maths
, asked on 5/5/18
Let
f
:
R
→
R
be such that
f
(
x
) = 2
x
. Determine:
(i) Range of
f
(ii) {
x
:
f
(
x
) = 1} (iii) whether
f
(
x + y
) =
f
(
x
)
f
(
y
) holds.
Answer
1
Eshita Rastogi
Subject: Maths
, asked on 5/5/18
Solve this:
Q EXAMPLES 8.
If ƒ : R
→
R be defined as follows :
ƒ (x) =
1
,
i
f
x
∈
Q
-
1
,
i
f
x
∉
Q
Find (i) ƒ (1/2), ƒ (
π
), ƒ
2
(ii) Range oƒƒ (iii) pre- images oƒ 1 and – 1.
Answer
1
Uma
Subject: Maths
, asked on 5/5/18
SIR WHAT DO YOU MEAN BY DEFINE A RELATION ON THE SET.
Q.17. Let A = {1, 2, 3, ....., 14}. Define a relation on a set A by R = {(x, y) : 3x - y = 0, where x, y
∈
A}. Depict relationship using an arrow diagram. Write down its domain, co-domain and range.
Q.18. Draw the graph of f (x) = | 2x + 3 | + 2 and find its domain & range.
Answer
1
Uma
Subject: Maths
, asked on 5/5/18
9. Draw the graph of (x) = |2x – 3|; x ∈ R; and find its domain & range.
10. If (x) and g(x) are two functions such that (x) = 3x – 1, g(x) = x
2
+ 2.
Find (i) (f + g) (x) (ii) (f – g) (x) (iii) (f. g) (x) (iv)
f
g
x
Answer
1
Uma
Subject: Maths
, asked on 5/5/18
f
: R → R is defined by
f
x
=
3
x
-
1
,
x
<
-
1
x
2
-
3
,
-
1
≤
x
≤
3
.
Find (i) f(0) (ii) f(–1) (iii) f(3)
Answer
1
Eshita Rastogi
Subject: Maths
, asked on 5/5/18
11and 12
Q11. Let A = {a, b}. List all relations on A and find their number.
Q12. Let A = { x, y, z) and B = { a, b}. Find the total number of relations from A into B.
Answer
1
Uma
Subject: Maths
, asked on 5/5/18
If (x) and g(x) are two functions such that (x) = 3x – 1, g(x) = x 2 + 2. Find (i) (f + g) (x) (ii) (f – g) (x) (iii) (f. g) (x) (iv) ( f /g )(x)
Answer
1
Uma
Subject: Maths
, asked on 5/5/18
6. f ∶ R → R is defined by f(x) = { 3x − 1, x < −1
x 2 − 3, −1 ≤ x ≤ 3. Find (i) f(0) (ii) f(-1) (iii) f(3)
Answer
1
Yatharth Patel
Subject: Maths
, asked on 4/5/18
Plz solve q5
Q.5. If P (x) is a polynomial of degree 3 such that P (i) =
1
i
+
1
∀
i = {1, 2, 3, 4}. Then find P (5)?
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Explain algebra of real functions
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Explain the Greatest integer function
Answer
1
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What are you looking for?
Example 15: Define the real valued function . Complete the Table given below using this definition. What is the domain and range of this function ?
Determine
(i) the image set of the domain of f
(ii) {x : f(x) = – 2}
(iii) whether f(xy) = f(x) + f(y) holds.
(i) Range of f (ii) {x : f(x) = 1} (iii) whether f(x + y) = f(x) f(y) holds.
Q EXAMPLES 8. If ƒ : R R be defined as follows :
ƒ (x) =
Find (i) ƒ (1/2), ƒ (), ƒ (ii) Range oƒƒ (iii) pre- images oƒ 1 and – 1.
Q.17. Let A = {1, 2, 3, ....., 14}. Define a relation on a set A by R = {(x, y) : 3x - y = 0, where x, y A}. Depict relationship using an arrow diagram. Write down its domain, co-domain and range.
Q.18. Draw the graph of f (x) = | 2x + 3 | + 2 and find its domain & range.
10. If (x) and g(x) are two functions such that (x) = 3x – 1, g(x) = x2 + 2.
Find (i) (f + g) (x) (ii) (f – g) (x) (iii) (f. g) (x) (iv)
Find (i) f(0) (ii) f(–1) (iii) f(3)
Q11. Let A = {a, b}. List all relations on A and find their number.
Q12. Let A = { x, y, z) and B = { a, b}. Find the total number of relations from A into B.
x 2 − 3, −1 ≤ x ≤ 3. Find (i) f(0) (ii) f(-1) (iii) f(3)
Q.5. If P (x) is a polynomial of degree 3 such that P (i) = i = {1, 2, 3, 4}. Then find P (5)?