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

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 ?

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -EXERCISE 1.2
  1. Show that the function f : R rarr R , defined by f(x) =1/x is one - o...

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  2. Check the injectiveity and surjectivity of the following functions : ...

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  3. Check the injectiveity and surjectivity of the following functions : ...

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  4. Check the injectiveity and surjectivity of the following functions : ...

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  5. Check the injectiveity and surjectivity of the following functions : ...

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  6. Check the injectiveity and surjectivity of the following functions : ...

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  7. Prove that the Greatest Integer Function f : R rarr R , given by f(x)...

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  8. Show that the Modulus Function f : R rarr R, given by f(x) = |x| , is ...

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  9. Show that the Signum Function f : R rarr R given by f(x) = {(1," if "...

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  10. Let A = {1,2,3},B = {4,5,6,7} and let f={(1,4),(2,5),(3,6)} be a funct...

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  11. In each of the following cases , state whether the function is one - o...

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  12. In each of the following cases , state whether the function is one - o...

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  13. Let A and B be sets. Show that f: A xxB rarr B xxA such that f(a,b) = ...

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  14. Let : f: N rarr N be defined by f(n)={{:((n+1)/2," if n is odd"),(n/2,...

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  15. Let A = R - {3} and B = R - {1}. Consider the function f : A rarrB def...

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  16. Let f : R rarrR be defined as f(x)=x^4 . Choose the correct answer.

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  17. Let f : R rarr R be defined as f(x) = 3x. Choose the correct answer.

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