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Consider `f : N ->N`, `g : N ->N`and `h : N ->R`defined as`f (x) = 2x`, `g (y) = 3y + 4`and `h (z) = s in z`, `AA`x, y and z in N. Show that ho(gof ) = (hog) of.

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LHS: `oh(gof)`
`gof=g(f(x))`
=`g(2x)`
=`3(2x)+4`
=`6x+4`
`oh(gof)=h(6x+4)`
=`sin(6x+4)`
RHS: `(hog)of`
...
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NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Let Y = {n^2: n in N} in N. Consider f : N ->Yas f(n)=n^2. Show tha...

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  2. Let f : N ->R be a function defined as f(x)=4x^2+12 x+15. Show that f...

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  3. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

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  4. Consider f : {1, 2, 3} ->{a , b , c}and g : {a , b , c} ->{a p p l e ,...

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

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

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  7. Let f : {1, 2, 3}->{a , b , c}be one-one and onto function given by f...

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  8. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , where...

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  9. Let S = {1, 2, 3}. Determine whether the functions f : S->S defi...

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  10. Show that addition, subtraction and multiplication are binary operati...

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  11. Consider the identity function IN : N->N defined as, IN(x)=x for al...

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  12. Let R be a relation on the set A of ordered pairs of positive integer...

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  13. Let X={1,2,3,4,5,6,7,8,9}. Let R be a relation in X given by R1={(x,y)...

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  14. Show that -ais not the inverse of a in Nfor the addition operation +...

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  15. If R1 and R2 are equivalence relations in a set A, show that R1nnR2 i...

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  16. Find the number of all one-one functions from set A = {1, 2, 3}to itse...

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  17. Let A={1,\ 2,\ 3} . Then, show that the number of relations containi...

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  18. Let f : X->Ybe a function. Define a relation R in X given by R = {(a ...

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  19. Determine which of the following binary operations on the set N are a...

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  20. Show that the number of equivalence relation in the set {1, 2, 3}cont...

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