Unit 1.1.3: Function
1. (a) Define inverse of function,
Solution:
If is one to one onto function then the new function defined from B ot A is called inverse function. It is denoted by .
(b) What is the relation between composition of a function and its inverse.
Solution:
The relation between composition of a function and its inverse is an identity function.
2. Represent the following functions in mapping diagram and find their inverse.
(a)
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(b)
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(c)
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3. If is the real - valued function, find
(a) (b) (c) (d) in each of the following:
(i)
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(ii)
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(iii)
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(iv)
Solution:
4. If find
(a) (b) . and are real-valued functions.
Solution:
5. (a) If and find the value of , \ \ are real-valued functions.
Solution:
5. (b) is real-valued function defined as . If then find the values of and .
Solution:
6. Write the formula of volume and surface area of sphere in terms of radius. Find the functional relation and write their inverse.
Solution:
(b)
Solution:
(c)
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3. If is the real - valued function, find
(a) (b) (c) (d) in each of the following:
(i)
Solution:
(ii)
Solution:
(iii)
Solution:
(iv)
Solution:
4. If find
(a) (b) . and are real-valued functions.
Solution:
5. (a) If and find the value of , \ \ are real-valued functions.
Solution:
5. (b) is real-valued function defined as . If then find the values of and .
Solution:
6. Write the formula of volume and surface area of sphere in terms of radius. Find the functional relation and write their inverse.
Solution: