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Let f: N->N be defined by: f(n)={(n+1)/2...

Let `f: N->N` be defined by: f(n)={(n+1)/2, if `n` is odd (n-1)/2, if `n` is even Show that `f` is a bijection.

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RD SHARMA ENGLISH-FUNCTION-All Questions
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  2. Show that f: R->R , given by f(x)=x-[x] , is neither one-one nor onto.

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

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

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  10. 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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  15. If f: Z->Z be defined by f(x)=2x for all x in Z . Find g: Z->Z such t...

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  16. Let f,\ g and h be functions from R to R . Show that (f+g)oh=foh+goh

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  17. Let f,\ g and h be functions from R to R . Show that (fog)oh=(foh)(goh...

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  18. Let f: R->R be the signum function defined as f(x)={1,\ x >0,\ \ \ \ 0...

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  19. Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx i...

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