1

Define a function as a set of ordered pairs.

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2

Define a function as a correspondence between two sets.

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3

What is the fundamental difference between a relation and function? Is every relation a function?

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4

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Let X = {1, 2, 3, 4,}, Y = {1, 5, 9, 11, 15, 16} and F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.

Are the following true?

(i) F is a relation from X to Y (ii) F is a function from X to Y. Justify your answer in following true?

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5

Let X = {-1, 0, 3, 7, 9} and f : X → R : f(x) x^{3} + 1. Express the function f as set of ordered pairs.

6

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Let A = {–1, 0, 1, 2} and B = {2, 3, 4, 5}. Find which of the following are function from A to B. Give reason.

(i) f = {(–1, 2), (-1, 3), (0, 4), 1,5)}

(ii) g = {(0, 2), (1, 3), (2, 4)}

(iii) h = {(-1, 2), (0, 3), (1, 4), (2, 5)}

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7

Let A = {1, 2} and B = {2, 4, 6}. Let f = {(x, y) : x ϵ A, y ϵ B and y > 2x + 1}. Write f as a set of ordered pairs. Show that f is a relation but not a function from A to B.

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8

Let A = {0, 1, 2} and B = {3, 5, 7, 9}. Let f = {(x, y) : x ϵ A, y ϵ B and y = 2x + 3}. Write f as a set of ordered pairs. Show that f is function from A to B. Find dom (f) and range (f).

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9

Let A = {2, 3, 5, 7} and B = {3, 5, 9, 13, 15}. Let f = {(x, y) : x ϵ A, y ϵ B and y = 2x – 1}. Write f in roster form. Show that f is a function from A to B. Find the domain and range of f.

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10

Let g = {(1, 2), (2, 5), (3, 8), (4, 10), (5, 12), (6, 12)}. Is g a function? If yes, its domain range. If no, give reason.

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11

Let f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a linear function from Z into Z. Write an expression for f.

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12

If f (x) = x^{2}, find the value of .

13

If f(x) = x^{2}, find the value of .

14

Let X = {12, 13, 14, 15, 16, 17} and f : A → Z : f(x) = highest prime factor of x. Find range (f)

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15

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Let R^{+} be the set of all positive real numbers. Let f : R^{+}→ R : f(x) = log_{e}x. Find

(i) range (f)

(ii) {x : x ϵ R^{+} and f(x) = -2}.

(iii) Find out whether f(x + y) = f(x). f(y) for all x, y ϵ R.

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16

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Let f : R → R : f(x) =2^{x}. Find

(i) range (f)

(ii) {x : f(x) = 1}.

(iii) Find out whether f(x + y) = f(x). f(y) for all x, y ϵ R.

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17

Let f : R → R : f(x) =x^{2} and g : C → C: g(x) =x^{2}, where C is the set of all complex numbers. Show that f ≠ g.

18

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f, g and h are three functions defined from R to R as following:

(i) f(x) = x^{2}

(ii) g(x) = x^{2} + 1

(iii) h(x) = sin x

That, find the range of each function.

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19

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Let f : R → R : f(x) = x^{2} + 1. Find

(i) f^{–1} {10}

(ii) f^{–1} {–3}.

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20

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The function is the formula to convert x °C to Fahrenheit units. Find

(i) F(0),

(ii) F(–10),

(iii) The value of x when f(x) = 212.

Interpret the result in each case.

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1

If f(x) = x^{2} – 3x + 4 and f(x) = f(2x + 1), find the values of x.

2

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(i)

(ii)

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3

If then show that

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4

If then show that f{f(x)} = x.

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5

If f(x) = and then prove that f{(x)} = , when it is given that .

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6

If then show that f [f{f(x)}] = x.

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7

If then show that f(tanθ) = sin 2θ.

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8

If , prove that x = f(y).

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1

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Find the domain of each of the following real function.

(i)

(ii)

(iii)

(iv)

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2

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Find the domain and the range of each of the following real function:

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3

Find the domain and the range of each of the following real function:

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4

Find the domain and the range of each of the following real function:

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5

Find the domain and the range of each of the following real function:

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6

Find the domain and the range of each of the following real function:

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7

Find the domain and the range of each of the following real function: f(x) =

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8

Find the domain and the range of each of the following real function: f(x) =

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9

Find the domain and the range of each of the following real function:

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10

Find the domain and the range of each of the following real function:

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11

Find the domain and the range of each of the following real function:

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12

Find the domain and the range of each of the following real function: f(x) = 1 – |x – 2|

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13

Find the domain and the range of each of the following real function:

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14

Find the domain and the range of each of the following real function:

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15

Find the domain and the range of each of the following real function:

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1

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Consider the real function f: R → R: f(x) = x + 5 for all

x ϵ R. Find its domain and range. Draw the graph of this function.

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2

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Consider the function f: R → R, defined by

Write its domain and range. Also, draw the graph of f(x).

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3

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Find the domain and the range of the square root function,

f: R^{+} U {0} → R f(x) = for all non-negative real numbers.

Also, draw its graph.

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4

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Find the domain and the range of the cube root function,

f: R → R: f(x) = x^{1/3} for all x ϵ R. Also, draw its graph.

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1

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Let f : R → R : f(x) = x + 1 and g : R → R : g(x) = 2x – 3.Find

(i) (f + g) (x)

(ii) (f – g) (x)

(iii) (fg) (x)

(iv)(f/g) (x)

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2

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Let f : R → R : f(x) = 2x + 5 and g : R → R : g(x) = x^{2} + x.

Find

(i) (f + g) (x)

(ii) (f – g) (x)

(iii) (fg) (x)

(iv) (f/g)(x)

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3

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. Let f: R → R: f(x) = x^{3} + 1 and g: R → R: g(x) = (x + 1). Find:

(i) (f + g) (x)

(ii) (f – g) (x)

(iii) (1/f) (x)

(iv) (f/g) (x)

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4

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. Let f: R → R; f(x)= ,where c is a constant. Find

(i) (cf) (x)

(ii) (c^{2} f) (x)

(iii)

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5

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. Let f:(2, ∞) → R: f(x) = and g: (2, ∞) → R: g(x) = Find:

(i) (f + g) (x)

(ii) (f - g) (x)

(iii) (fg) (x)

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1

Find the set of values for which the function f(x) = 1 – 3x and g(x) = 2x^{2} – 1 are equal.

2

Find the set of values for which the function f(x) = x + 3 and g(x) = 3x^{2} – 1 are equal.

3

Let X = {–1, 0, 2, 5} and f : X → R Z: f(x) = x^{3} + 1. Then, write f as a set of ordered pairs.

4

Let A = {–2, –1, 0, 2} and f : A → Z: f(x) = x^{2} – 2x – 3. Find f(A).

5

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Let f : R → R : f(x) = x^{2}.

Determine (i) range (f) (ii) {x : f(x) = 4}

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6

Let f : R → R : f(x) = x^{2} + 1. Find f^{–1} {10}.

7

Let f : R^{+} → R : f(x) = log_{e} x. Find {x : f(x) = –2}.

8

Let A = {6, 10, 11, 15, 12} and let f : A → N : f(n) is the highest prime factor of n. Find range (f).

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9

Find the range of the function f(x) = sin x.

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10

Find the range of the function f(x) = |x|.

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11

Write the domain and the range of the function,.

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12

If then find dom (f) and range (f).

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13

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Let f = {(1, 6), (2, 5), (4, 3), (5, 2), (8, –1), (10, –3)} and g = {(2, 0), (3, 2), (5, 6), (7, 10), (8, 12), (10, 16)}.

Find (i) dom (f + g) (ii) dom .

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14

If , find the value of .

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15

If , where x ≠ –1 and f{f(x)} = x for x ≠ –1 then find the value of k.

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16

Find the range of the function, .

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17

Find the domain of the function, f(x) = log |x|.

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18

If = for all x ϵ R – {0} then write an expression for f(x).

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19

Write the domain and the range of the function,.

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20

Write the domain and the range of the function, f(x) = .

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21

Write the domain and the range of the function, f(x) = –|x|.

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