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Show that if f : A ->B and g : B ->Care ...

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

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To show that if \( f: A \to B \) and \( g: B \to C \) are onto functions, then the composition \( g \circ f: A \to C \) is also onto, we will follow these steps: ### Step 1: Understand the Definition of Onto Functions An onto function (or surjection) is defined such that for every element \( y \) in the codomain \( Y \), there exists at least one element \( x \) in the domain \( X \) such that \( h(x) = y \). ### Step 2: Given Functions We are given two functions: - \( f: A \to B \) is onto, meaning for every \( b \in B \), there exists \( a \in A \) such that \( f(a) = b \). ...
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NCERT ENGLISH-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Show that if f : A ->B and g : B ->Care onto, then gof : A ->C is als...

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  2. Show that if f : A ->Band g : B ->Care one-one, then gof : A ->Cis al...

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  3. Let f : {2, 3, 4, 5}-> {3, 4, 5, 9}and g : {3, 4, 5, 9} ->{7, 11 , 15}...

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  4. Show that a one-one function f : {1, 2, 3}-> {1, 2, 3}must be onto.

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  5. Show that if f: R-{7/5}->R-{3/5}is defined by f(x)=(3x+4)/(5x-7)an...

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  6. Find gof and fog, if f : R ->Rand g : R ->Rare given by f(x) = cos xan...

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  7. Show that the function f: R->R , defined as f(x)=x^2 , is neither one-...

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  8. Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for e...

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  9. If A={1,\ 2,\ 3} , show that an onto function f: A->A must be one-o...

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  10. Show that f\ : NvecN ,\ given by f(x)={x+,\ \ \ \ \ \ \ \ \ \ \ \ \ ...

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  11. Show that the function f: N->N , given by f(x)=2x , is one-one but not...

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  12. Prove that f: R->R , given by f(x)=2x , is one-one and onto.

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  13. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

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  14. Let A be the set of all 50 students of class X I I in a central scho...

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  15. Show that the relation R in the set {1, 2, 3}given by R = {(1, 1), (2...

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  16. Show that the relation R on the set Z of integers, given by R={(a ,\ b...

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  17. Let T be the set of all triangles in a plane with R a relation in T g...

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  18. Let L be the set of all lines in a plane and R be the relation in L de...

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  19. Let A be the set of all students of a boys school. Show that the rela...

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  20. Show that a is the inverse of a for the addition operation + on R a...

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