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Show that the function f: R-{3}->R-{1} g...

Show that the function `f: R-{3}->R-{1}` given by `f(x)=(x-2)/(x-3)` is a bijection.

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Classify f: R->R , defined by f(x)=x/(x^2+1) as injection, surjecti...

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  2. If f: A->B is an injection such that range of f={a} . Determine the...

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  3. Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is a ...

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  4. Let A=[-1,\ 1] . Then, discuss whether the following functions from...

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  5. Are the following set of ordered pairs functions? If so, examine wh...

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  6. Let A={1,\ 2,\ 3} . Write all one-one from A to itself.

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  7. If f: R->R be the function defined by f(x)=4x^3+7 , show that f is a b...

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  8. Show that the exponential function f: R->R , given by f(x)=e^x , is...

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  9. Show that the logarithmic function f: R0+->R given by f(x)=(log)a x...

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  10. Show that a one-one function f : {1, 2, 3}-> {1, 2, 3}must be onto.

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  11. If A={1,\ 2,\ 3} , show that an onto function f: A->A must be one-o...

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

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  13. Give examples of two one-one functions f1 and f2 from R to R such t...

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  14. Give examples of two surjective function f1 and f2 from Z to Z such...

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  15. Show that if f1 and f2 are one-one maps from R to R , then the product...

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  16. Suppose f1 and f2 are non-zero one-one functions from R to R . Is (...

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  17. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

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  18. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

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  19. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

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  20. Show that f: R->R , given by f(x)=x-[x] , is neither one-one nor onto.

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