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अर्कज
Subject: Maths
, asked on 6/5/18
$Letf\left(x\right)={x}^{2}andg\left(x\right)=2x+1betworealfunctions.Find\phantom{\rule{0ex}{0ex}}(f+g)\left(x\right),(f-g)\left(x\right),\left(fg\right)\left(x\right),\left(\frac{f}{g}\right)\left(x\right)$
Answer
1
अर्कज
Subject: Maths
, asked on 6/5/18
Example 15:
Example 15: Define the real valued function
$\mathrm{f}:\mathrm{R}-\left\{\mathrm{o}\right\}\to \mathrm{R}\mathrm{defined}\mathrm{by}\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\mathrm{x}},\mathrm{x}\in \mathrm{R}-\left\{0\right\}$
. 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
$y=\frac{1}{x}$
...
...
...
...
...
...
...
...
...
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
$\to $
R be defined as follows :
ƒ (x) =
$\left\{\begin{array}{ccc}1,& if& x\in Q\\ -1,& if& x\notin Q\end{array}\right.$
Find (i) ƒ (1/2), ƒ (
$\mathrm{\pi}$
), ƒ
$\left(\sqrt{2}\right)$
(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
$\in $
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)
$\left(\frac{f}{g}\right)\left(x\right)$
Answer
1
Uma
Subject: Maths
, asked on 5/5/18
f
: R → R is defined by
$f\left(x\right)=\left\{\begin{array}{l}3x-1,x-1\\ {x}^{2}-3,-1\le x\le 3\end{array}\right.$
.
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) =
$\frac{1}{i+1}\forall $
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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Example 15: Define the real valued function $\mathrm{f}:\mathrm{R}-\left\{\mathrm{o}\right\}\to \mathrm{R}\mathrm{defined}\mathrm{by}\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\mathrm{x}},\mathrm{x}\in \mathrm{R}-\left\{0\right\}$. Complete the Table given below using this definition. What is the domain and range of this function ?

$y=\frac{1}{x}$

f: R^{+}→ R, where R^{+}is the set of all positive real numbers, be such thatf(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.f:R→Rbe such thatf(x) = 2^{x}. Determine:(i) Range of

f(ii) {x:f(x) = 1} (iii) whetherf(x + y) =f(x)f(y) holds.Q EXAMPLES 8.If ƒ : R $\to $R be defined as follows :ƒ (x) = $\left\{\begin{array}{ccc}1,& if& x\in Q\\ -1,& if& x\notin Q\end{array}\right.$

Find (i) ƒ (1/2), ƒ ($\mathrm{\pi}$), ƒ $\left(\sqrt{2}\right)$ (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 $\in $ 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) = x

^{2}+ 2.Find (i) (f + g) (x) (ii) (f – g) (x) (iii) (f. g) (x) (iv) $\left(\frac{f}{g}\right)\left(x\right)$

f: R → R is defined by $f\left(x\right)=\left\{\begin{array}{l}3x-1,x-1\\ {x}^{2}-3,-1\le x\le 3\end{array}\right.$.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) = $\frac{1}{i+1}\forall $ i = {1, 2, 3, 4}. Then find P (5)?