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Show that if f1 and f2 are one-one maps ...

Show that if `f_1` and `f_2` are one-one maps from `R` to `R` , then the product `f_1xxf_2: R->R` defined by `(f_1xxf_2)(x)=f_1(x)f_2(x)` need not be one-one.

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Give examples of two one-one functions f1 and f2 from R to R such t...

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

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

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

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

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

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

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

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  9. Let f: N->N be defined by: f(n)={(n+1)/2, if n is odd (n-1)/2, if n i...

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  10. Let R be the set of real numbers. If f: R->R :f(x)=x^2 and g: R->R ...

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  11. Let : R->R ; f(x)=sinx and g: R->R ; g(x)=x^2 find fog and gof .

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  12. Let f:{2,3,4,5}vec{3,4,5,9}a n dg:{3,4,5,9}vec{7, 11 , 15} be function...

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  13. Let f:{1,\ 3,4\ }->{1,\ 2,\ 5} and g:{1,\ 2,\ 5}->{1,\ 3} be given by ...

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  14. Find gof and fog , if f: R->R and g: R->R are given by f(x)=|x| and g(...

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  15. If the functions f and g are given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} ...

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  16. If the function f: R->R be given by f(x)=x^2+2 and g: R->R be given by...

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  17. If f: R-{7/5}->R-{3/5} be defined as f(x)=(3x+4)/(5x-7) and g: R-{3/5}...

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  18. Find the derivative of f(x) = x^2- 3x + 2.

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  19. If f,g: R -R are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fi...

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  20. Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=IZ .

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