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Show that the function f:N rarr N , give...

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

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Prove that the function f :R rarr R , given by f(x) = 2x, is one-one and onto.

Show that the function f : R rarr R , defined by f(x) =1/x is one - one and onto , where R is the set of all non - zero real number . is the result true, if the domain R is replaced by N with co-domain being same as R ?

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

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

Show that the Modulus Function f : R rarr R , given by f(x) = |x| , is neither oneone nor onto , where |x| is x, if x is positive or 0 and |x| is - x , if x is negative.

Show that the function f:N rarr N , given by f(1) = f(2) = 1 and f(x) = x - 1, for every x gt 2 , is onto but not one-one.

Prove that the Greatest Integer Function f : R rarr R , given by f(x) = [x] , is neither one - one nor onto , where [x] denotes the greatest integer less than or equal to x.

Show that the function given by f(x)=e^(2x) is increasing on R.

Show that f : [-1,1] rarr R , given by f(x) = (x)/(x+2) is one - one . Find the inverse of the function f:[-1,1] rarr Range f. (Hint: For y in Range f,y=f(x) = x/(x+2) , for some x in [-1,1] , i.e., x = (2y)/(1-y) ).

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Let R be the realtion defined in the set A = {1,2,3,4,5,6,7} by R ={(a...

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  2. Let A be the set of all 50 students of Class X in a school. Let f : A ...

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  3. Show that the function f:N rarr N , given by f(x) = 2x, is one-one but...

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  4. Prove that the function f :R rarr R , given by f(x) = 2x, is one-one a...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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