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Are f and g both necessarily onto, if gof is onto ?

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

Show that if f:A to B and g: B to C are onto, then gof :A to C is also onto.

Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| for all xdot Then g is a. Onto if f is onto b. One-one if f is one-one c. Continuous if f is continuous d. None of these

Show that if f: A to B and g : B to C are one-one, then gof :A to C is also one-one.

Give examples of two functions f : N to N and g : N to N such g o f is onto but f is not onto.

For real x, let f(x)""=""x^3+""5x""+""1 , then (1) f is oneone but not onto R (2) f is onto R but not oneone (3) f is oneone and onto R (4) f is neither oneone nor onto R

Let the functions f: QQ rarr QQ and g: QQ rarr QQ be defined by, f(x)=3x and g(x)=x+3 . Assuming that f and g are both invertible , verify that , ( g o f) ^(-1) =(f^(-1) o g ^(-1)) .

Let f:XtoY be a function defined by f(x)=asin(x+pi/4)+bcosx+c . If f is both one-one and onto, find sets X and Y.

Let f(x) and g(x) be one-one onto functions where f : {a,b,c,d} rarr {1,2,3,4} and g : {3,4,5,6} rarr {w,x,y,z} respectively. The number of elements in the range set of g (f(x)) are

Let A ={a,b,c} and B={p,q,r,}, defined three one-one and onto mappings from A to B and also find their inverse mappings

NCERT BANGLISH-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Are f and g both necessarily onto, if gof is onto ?

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  2. Let f : R to R be defined as f (x) =10 x +7. Find the function g : R t...

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  3. Let f:Wto W be defined as f (n)=n -1, if n is odd and f (n) =n +1, if ...

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  4. If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

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  5. Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f...

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  6. Show that the function f: R to R given by f (x) = x ^(3) is injective...

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  7. Give examples of two functions f:N to Z and g: Z to Z such that g o f ...

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  8. Give examples of two functions f : N to N and g : N to N such g o f is...

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  9. Given a non empty set X, consider P (X) which is the set of all subset...

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  10. Given a non-empty set X, consider the binary opertion **: P(X) xx P (Y...

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  11. Find the number of all onto functins from the set {1,2,3..,n} to itsel...

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  12. Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S...

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  13. Show that +:R×R→R and o:R×R→R defined as a∗b=∣a−b∣ and aob=a for all a...

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  14. Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as ...

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  15. Define a binary opertion ** on the set {0,1,2,3,4,5} as a**b ={{:(a+...

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  16. Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defin...

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  17. Let A={1,2,3}. Then the number of relations containing (1,2) and (1,3)...

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  18. Let A = {1,2,3},B={5,6.7} then find AcapB

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  19. Let f: R → R be the Signum Function defined as f(x)={ 1, x>0 0, x=0−1,...

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  20. Number of binary opertions on the set {a,b} are

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