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If f(x)=x^3-1/(x^3) , show that f(x)+f(1...

If `f(x)=x^3-1/(x^3)` , show that `f(x)+f(1/x)=0.`

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RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. Let cb ea non-zero real number and f: RvecR be a function defined by f...

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  2. If f(x)=1/(1-x) , show thatf[f{f(x)}]=xdot

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  3. If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

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  4. Let fa n dg be two real functions defined by f(x)=1/(x+4)a n dg(x)=(x-...

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  5. Find the range of each of the following functions: f(x)=1/(sqrt(x-5)) ...

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  6. Find the domain of the real function f(x) defined by f(x)=sqrt((1-|x|)...

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  7. Let f be the exponential function and g be the logarithmic function, F...

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  8. If f is a real function satisfying f(x+1/x)=x^2+1/(x^2) for all x in ...

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  9. Let f\ be a relation on the set NN of natural numbers defined by f={(...

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  10. Let f be the subset of Z xxZ defined by f" "=" "{(a b ," "a" "+" "b)" ...

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  11. Consider a rule f(x)=2x-3 associating elements of NN (set of natural n...

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  12. Let A={-2,\ -1,\ 0,\ 1,\ 2}a n d\ f: A->ZZ be given y f(x)=x^2-2x-3. F...

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  13. Let A={1,2},\ B={3,6} and f: A->B given by f(x)=x^2+2\ and\ g: A->B gi...

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  14. Let f : R - {2} rarr R be defined as f(x) = (x^2 - 4)/(x-2) and g: R...

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  15. Let f: ZZ->ZZ\ a n d\ g: ZZ->ZZ\ be functions defined by f={(n , n^2)...

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  16. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){-5}

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  17. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){26}

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  18. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){10 , 37}

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  19. Let f" "=" "{(1,1)," "(2," "3)," "(0, -1)," "(-1," "-3)} be a function...

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  20. If f: RR->RR be defined as follows: f(x)={1,\ if\ x in QQ, -1,\ if\...

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