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Q5 (3)  Find the range of each of the following functions.

f (x) = x, x is a real number

Given function is  It is given that  x is a real  number Therefore, Range of function   is  R

Q5 (2)  Find the range of each of the following functions

$f ( x ) = x ^2 +2$ , x is a real number.

Given function is  It is given that  x is a real  number Now, Add 2 on both the sides  Therefore, Range of function  is

Q5 (1)  Find the range of each of the following functions.

$f (x) = 2 - 3x, x \epsilon R, x > 0.$

Given function is  It is given that  Now, Add 2 on both the sides  Therefore, Range of function  is

Q4(4)    The function ‘t’ which maps temperature in degree Celsius into temperature in
degree Fahrenheit is defined by $t ( C ) = \frac{9 C }{5} + 32$
The value of C, when t(C) = 212.

Given function is  Now, Therefore, When t(C) = 212 , value of C is  100

Q4(3)    The function ‘t’ which maps temperature in degree Celsius into temperature in
degree Fahrenheit is defined by $t ( C ) = \frac{9 C }{5} + 32$
t (-10)

Given function is  Now, Therefore, Value of t(-10) is  14

Q4(2)    The function ‘t’ which maps temperature in degree Celsius into temperature in
degree Fahrenheit is defined by $t ( C ) = \frac{9 C }{5} + 32$
t (28)

Given function is  Now, Therefore, Value of t(28) is

Q4(1)    The function ‘t’ which maps temperature in degree Celsius into temperature in
degree Fahrenheit is defined by $t ( C ) = \frac{9 C }{5} + 32$
t (0)
.

Given function is  Now, Therefore, Value of t(0) is 32

Q3   A function f is defined by f(x) = 2x –5. Write down the values of f (-3)

Given function is  Now, Therefore, Value of f(-3) is -11

Q3 (2)  A function f is defined by f(x) = 2x –5. Write down the values of f (7)

Given function is  Now, Therefore, Value of f(7) is 9

Q3 (1)   A function f is defined by f(x) = 2x –5. Write down the values of
f (0),

Given function is  Now, Therefore, Value of f(0) is -5

Q2 (2)  Find the domain and range of the following real functions:

$f ( x ) = \sqrt { 9- x ^2 }$

Given function is  Now, Domain: These are the values of x for which f(x) is defined. for the given f(x) we can say that, f(x) should be real and for that,9 - x2 ≥ 0 [Since a value less than 0 will give an imaginary value] Therefore, The domain of f(x) is   Now, If  we put the value of x from   we will observe that the value of function   varies from 0 to 3 Therefore, Range of f(x) is

Q2  Find the domain and range of the following real functions:

$f (x ) = - |x|$

Given function is  Now,  we know that Now, for a function f(x), Domain: The values that can be put in the function to obtain real value. For example f(x) = x, now we can put any value in place of x and we will get a real value. Hence, the domain of this function will be Real Numbers. Range: The values that we obtain of the function after putting the value from domain. For Example: f(x) = x +...

Q1 (3)  Which of the following relations are functions? Give reasons. If it is a function,
determine its domain and range.

{(1,3), (1,5), (2,5)}.

Since the same first element 1 corresponds to two different images 3 and 5. Hence, this relation is not a function.

Q1 (2)  Which of the following relations are functions? Give reasons. If it is a function,
determine its domain and range.

{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}

Since, 2, 4, 6, 8, 10,12 and 14 are the elements of domain R having their unique images. Hence, this relation R is a function.   Now, As Domain of R = set of all first elements of the order pairs in the relation. Therefore, Domain of   Now, As Range of R = set of all second elements of the order pairs in the relation. Therefore, Range of   Therefore, domain and range of R are    respectively

Q1 (1)  Which of the following relations are functions? Give reasons. If it is a function,
determine its domain and range.

{(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}

Since, 2, 5, 8, 11, 14 and 17 are the elements of domain R having their unique images. Hence, this relation R is a function. Now, As Domain of R = set of all first elements of the order pairs in the relation. Therefore, Domain of   Now, As Range of R = set of all second elements of the order pairs in the relation. Therefore, Range of  Therefore, domain and range of R are    respectively
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