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Show that the function f: R rarr R , def...

Show that the function f: `R rarr R` , defined as `f(x) = x^2` , is neither one-one nor onto.

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

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Prove that the function f :R rarr R , given by f(x) = 2x, is one-one a...

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  2. Show that the function f:N rarr N , given by f(1) = f(2) = 1 and f(x) ...

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  3. Show that the function f: R rarr R , defined as f(x) = x^2 , is neithe...

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  4. Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1...

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  5. Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one...

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  6. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be ont...

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  7. Let f: {2, 3, 4, 5} rarr {3, 4, 5, 9} and g : {3, 4, 5, 9} rarr {7, 1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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