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Show that if f: R - {7/5} rarr R - {3/5}...

Show that if `f: R - {7/5} rarr R - {3/5} ` is defined by `f(x) = (3x+4)/(5x-7) and g: R - {3/5} rarr R - {7/5} ` is defined by `g(x) = (7x +4)/(5x-3) ` , then fog `=I_A and gof = I_(B) ,` where `A = R - {3/5} , B = R - {7/5} , I_(A) (x) = x, AA x in A , I_(B) (x) = x, AA x in B` are called identity functions on sets A and B , respectively .

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Let f: {2, 3, 4, 5} rarr {3, 4, 5, 9} and g : {3, 4, 5, 9} rarr {7, 1...

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  2. Find gof and fog, if f:R rarr R and g: R rarrR are given by f(x) = c...

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

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  4. Show that if f: A rarr B and g: B rarr C are one- one, then gof: A ra...

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  5. Show that if f: A rarr B and g: B rarr C are onto, then gof: A rarr ...

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

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  7. Are fand g both necessarily onto, if gof is onto?

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

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  9. Let f:N rarr Y be a function defined as f(x) = 4x + 3, where, Y = { y...

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  10. Let Y = {n^(2) :n in N} subN Consider f: N rarr Y as f(n) = n^2 . Sh...

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  11. Let f':N rarr R be a function defined as f'(x) = 4x^(2) + 12x + 15 . ...

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  12. Consider f: N rarr N,g :N rarr N and h: Nrarr R defined as f(x) = 2x, ...

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  13. Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} de...

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  14. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  15. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  16. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  17. Show that addition, subtraction and multiplication are binary operatio...

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  18. Show that subtraction and division are not binary operations on N.

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  19. Show that ** :Rxx R rarr R given by (a, b) rarr a + 4b^(2) is a bina...

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  20. Let P be the set of all subsets of a given set X. Show that cup: P xxP...

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