Let f: R → R and g: R → R be two function such that fog(x) = sin x – InterviewSolution

1.

Let f: R → R and g: R → R be two function such that fog(x) = sin x2 and gof(x) = sin2 x. find g(x) and g(x).

Answer»

Given, (fog)(x) = sin x² and (gof)(x) = sin² x

f(g(x)) = sin(x²) & g(f(x)) = (sin x)² ...(1)

Clearly, f(x) = sin x & g(x) = x²satisfies both conditions of (1)

So, f(x) = sin x and f(x) = x²

Discussion

No Comment Found

Related InterviewSolutions

What were the two main occupations of the Rig Vedic Aryans?
Name the two political institutions which exercised check on the powers of the King in the Rig Vedic period.
What w’as the position of women in the Rig Vedic age ?
Describe the social life of the Rig Vedic Aryans with reference to the following: (a) The Family Structure (b) Position of Women (c) Varna System
With reference to the following explain the main features of the Rig Vedic Economy: (a) Agriculture (b) Domestication of Animals (c) Trade Transactions, Crafts and Transportation
Mention any two archaeological sources to reconstruct the later Vedic Age.
Mention any two of the Ashrams in the life of a man in Aryan society.
What information do we gather from the later Vedic literature in respect of: (a) Spread of Vedic Civilization to many New Regions. (b) Role of Iron in later Vedic Economy.
Mention briefly the rituals and sacrifices of the later Vedic Aryans?
What is the message of the Bhagavad Gita?