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

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`x _(1) =x_(2)`
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If functions f : A rarr B and g : B rarr A satisfy gof = I_A , then show that f is one one and g is onto.

For functions f: A rarr B and g : B rarr A , gof = I_A . Prove that f is one one and g onto functions .

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

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If f : A rarr B and g : B rarr C be the bijective functions , then (gof)^(-1) is ..........

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NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Show that if f : A ->Band g : B ->Care one-one, then gof : A ->Cis al...

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  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

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

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

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  5. Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...

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  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

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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. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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

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

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  11. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

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

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  13. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

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

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  15. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

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  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

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  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

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  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

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  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

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  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

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