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The inverse of the function (1 0^x-1 0^(...

The inverse of the function `(1 0^x-1 0^(-x))/(1 0^x+1 0^(-x))` is

A

`(1)/(3)"log"_(10)(1+x)/(1-x)`

B

`(1)/(2)"log"_(10)(2+3x)/(2-3x)`

C

`(1)/(3)"log"_(10)(2+3x)/(2-3x)`

D

`(1)/(6)"log"_(10)(2-3x)/(2+3x)`

Text Solution

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The correct Answer is:
B
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DISHA PUBLICATION-RELATIONS AND FUNCTIONS-2-EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 3: Composite Function and Relation, Inverse of a Function, Binary Operations)
  1. If f(x) = x/(sqrt(1+x^2) then fofof(x)

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  2. If f(x)=|x| and g(x)=[x] then value of fog (-(1)/(4))+ gof (-(1)/(4)) ...

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  3. The inverse of the function (1 0^x-1 0^(-x))/(1 0^x+1 0^(-x)) is

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  4. Let f:[4,oo)to[4,oo) be defined by f(x)=5^(x^((x-4))).Then f^(-1)(x) i...

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  5. If the binary operation * on the set of integers Z , is defined by ...

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  6. If R sub A xx B and S sub B xx C be two relations, then (SoR)^-1 =

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  7. The binary operation * defined on N by a*b=a+b+a b for all a ,\ b in...

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  8. If f: R to R, g: R to R and h: R to R is such that f(x)=x^(2), g(x)= t...

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  9. Let f:[-pi/3,(2pi)/3]vec[0,4] be a function defined as f(x)=sqrt(3)sin...

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  10. If f(x)=1+x+x^2+x^3+....oo for |x| < 1 then f^-1(x)=

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  11. Let f be a function with domain X and range Y. Let A, B sube X and C, ...

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  12. If a binary operation * is defined by a*b=a^2+b^2+a b+1 , then (2*3...

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  13. A binary operation * on the set {0,1,2,3,4,5} is defined as: a*b={...

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  14. Let * be a binary operation on N given by a*b=H C F\ (a ,\ b),\ \ a...

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  15. Show that the total number of binary operation from set A to A is n^(n...

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  16. If fQ to Q f(x)=2x,g,Q to Q, g (x)=x+2 then value of (fog)^(-1)(20) is

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  17. If g(x)=x-2 is the inverse of the function f(x)=x+2, then graph of g(x...

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  18. Which of the following is not a binary operation on the indicated set?

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  19. If f(x) = -1 +|x-1|, -1 le x le 3 " and " g(x)=2-|x+1|, -2 le x le 2, ...

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  20. Let f(x)=(ax+b)/(cx+d). Then the fof (x) =x provided that

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