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Let A={12 ,13 ,14 ,15 ,16 ,17}a n df: Av...

Let `A={12 ,13 ,14 ,15 ,16 ,17}a n df: AvecZ` be function given by `f(x)=` highest prime factor of `x` . Find range of `fdot`

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Highest prime factors of `12, 13, 14, 15, 16, 17` are `3, 13, 7, 5, 2, 17`
So,
range `(f)={3,13,7,5,2,17}`
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RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. If f(x)=x+1/x , prove that [f(x)]^3=f(x^3)+3f(1/x)dot .

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  2. Let f: RvecRa n dg: CvecC be two functions defined as f(x)=x^2a n dg(x...

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  3. Let A={12 ,13 ,14 ,15 ,16 ,17}a n df: AvecZ be function given by f(x)=...

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  4. Find the domain of each of the following functions given by f(x)=1/(sq...

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  5. Find the domain of definition of the following f(x) given by f(x)=log4...

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  6. Find the domain of definition of the function f(x) given by f(x)=1/(lo...

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  7. Find the range of each of the following functions: f(x)=|x-3| f(x)...

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  8. Find the sum and product of identity function and the modulus function...

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

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

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

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

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

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

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

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  16. 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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  17. 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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  18. Let f : R - {2} rarr R be defined as f(x) = (x^2 - 4)/(x-2) and g: R...

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

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

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