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Relations and F...

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  • Question 1
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    Find the domain of the function defined as $$f(x)=\dfrac{1}{1-x^2}$$.

  • Question 2
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    If $$aN = (ax/x \ \epsilon \ N)$$ and $$bN \cap cN = dN,$$, where $$b, c \ \epsilon N$$ are relatively prime, then 

  • Question 3
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    Let $$f\left( x \right) :\begin{cases} x,\quad x\quad is\quad rational \\ 0,\quad x\quad is\quad irrational \end{cases}$$
    and 
    $$g\left( x \right) :\begin{cases} 0,\quad x\quad is\quad rational \\ x,\quad x\quad is\quad irrational \end{cases}$$

    If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$, then $$(f-g)$$ is

  • Question 4
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    If $$f:R \to R$$ is a function satisfying $$f(x + y) = f(xy)$$ for all $$x, y \in R$$ and $$f\left(\dfrac{3}{4}\right) = \left( \dfrac{3}{4} \right)$$ , then $$f\left( \dfrac{9}{16} \right)$$ =

  • Question 5
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    Find the domain of the function defined as $$f(x)=\dfrac{x+1}{2x+3}$$.

  • Question 6
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    Let R be a relation from$$ A=\left\{ 1,2,3,4 \right\}  to B=\left\{ 1,3,5 \right\}$$  such that $$R=[(a,b):a<b,where\ a\epsilon A\ and\ b\epsilon B]$$. What is $$R$$ equal to?

  • Question 7
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    $$x*y=\sqrt {\dfrac {(x+y)(y^{2}-12x)}{(x-2)(y-7)}}$$ then what will be the value of $$5*9$$?

  • Question 8
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    If $$f:R \rightarrow S$$ defined by $$f(x)=\sin x-\sqrt {3} \cos x+1$$ is onto, then the interval of $$S$$ is 

  • Question 9
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    If $$f:R\rightarrow R$$ is defined by $$ f\left( x \right) =\left| x \right| $$, then:

  • Question 10
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    If $$f:\,R\, \to R\,$$ is an even function which is differentiable on R and $${f^N}\left( \pi  \right) = 1\,the\,{f^N}\left( { - \pi } \right)\,{\rm{is}}$$

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