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Give examples of two functions `f:" "N->Z" "a n dg:" "Z->Z` such that o f is injective but is not injective. (Hint: Consider `f(x)" "=" "x" "a n d""""""""g(x)" "=" "|x|` )

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The correct Answer is:
`f(x)=x and g(x)=|x|`
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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Objective Type Questions (D. Very Short Answer Types Questions)
  1. If f is a function from RrarrR such that f(x)=x^(2)AA x inR, then show...

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  2. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

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  3. The function P is defined as: ''To each person on the earth is assig...

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  4. Write the function whose graph is shown below:

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  5. Consider functions f and g such that composite gof is defined and i...

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  6. Are f and g both necessarily onto, if gofis onto?

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  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  8. Give examples of function: f:NrarrN and g:NrarrN such that gof is ...

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  9. Find fog, if f:RrarrR and g:RrarrR are given by: f(x)=cosxandg(x)=x^...

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  10. If f (x) = sin x, g(x) = x^(2), if x inR, then find [(fog)(x)].

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  11. If f:RrarrR is defined by f(x)=3x+1, find f(f(x)).

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  12. Let '**' be a binary operation on N given by: a**b=LCM (a,b) for all...

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  13. Let '**' be a binary operation on N given by: a**b=LCM (a,b) for all...

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  14. The binary operation **:RxxRrarrR is defined as: a**b=2a+b. Find (...

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  15. Show that + : R xx R ->Rand xx : R xx R ->Rare commutative binary ope...

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  16. Show that + : R xx R ->Rand xx : R xx R ->Rare commutative binary ope...

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  17. Show that addition and multiplication are associative binary operat...

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  18. Show that subtraction and division are not binary operations on N.

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  19. Show that " "a is not the inverse of a in N for the addition op...

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  20. Show that " "a is not the inverse of a in N for the addition op...

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