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Consider functions f and g such that com...

Consider functions f and g such that composite gof is defined and is one-one. Are f and g both necessarily one-one.

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The correct Answer is:
g in not one-one
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Are f and g both necessarily onto,if gof is onto?

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Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

Prove that the function f: R^(+) to R which is defined as f(x)=log_(e) x is one - one .

Check whether the function F : R to R defined as F(X ) =x^2 is one-one or not.

Formula f(x)=x^2 defines a one-one function when

Examine the function f:R rarr R be defined by f(x)=3-4x is one one,onto and one one onto.

the function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

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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