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If f(x) = loge ((1+x)/(1-x)), prove that...

If `f(x) = log_e ((1+x)/(1-x))`, prove that `f((2x)/(1+x^2))=2f(x)`.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. Let R be a relation from N to N defined by R = {(a, b) : a, b in N and...

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  2. The relation 'f' is defined by f(x)={(x^2,0lexle3), (3x, 3lexle10):} ...

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  3. If f(x) = loge ((1+x)/(1-x)), prove that f((2x)/(1+x^2))=2f(x).

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  4. If f (x)= (2x)/(1+x^2), prove that f (tan theta)=sin 2 theta.

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  5. If f(x) = loge x, x > 0, prove that : f (uvw) = f (u) + f (v) +f (w).

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  6. Is the function: f(x)= (x^2-8x+18)/(x^2+4x+30) one-one ?

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  7. Prove that f: (-1, 1) rarr R defined by , f(x)= {(x/(1+x),-1<x<0),(0,x...

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  8. Let f: N rarr N be defined by : f(n)= {(n+1, if n is odd),(n-1, if n ...

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  9. Let f: N uu {0} rarr N uu {0} be defined by : f(n)= {(n+1, if n is ev...

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  10. The set of numbers which are mutiples of 5 is :

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  11. The set of prime numbers less than 100 is :

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  12. The set of circles passing through (0, 0) is :

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  13. The set A uu A’ is:

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  14. The set A nn A’ is:

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  15. The set phi is

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  16. Let A = {1, 2}, B= {3, 4}, then the number of relations from A to B wi...

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  17. Let A = {x, y,z} and B = {1,2}. Find the number of relations from A to...

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  18. A function 'f' is defined by f(x) = 2x - 5, find : f(-3).

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  19. If U ={1,2, 3, 4,5, 6,7,8, 9,10} and A= {3, 4, 7, 9}, then A’ equals :

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  20. If A= {1,2,3,4,5,6,7} and B= {7,8,9,10}, then A-B equals :

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