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Let f:[-pi/3,(2pi)/3]vec[0,4] be a funct...

Let `f:[-pi/3,(2pi)/3]vec[0,4]` be a function defined as `f(x)=sqrt(3)sinx-cosx+2.` Then `f^(-1)(x)` is given by `sin^(-1)((x-2)/2)-pi/6` `sin^(-1)((x-2)/2)+pi/6` `(2pi)/3+cos^(-1)((x-2)/2)` (d) none of these

A

`sin((x-2)/(2))-(pi)/(6)`

B

`sin((x-2)/(2))+(pi)/(6)`

C

`(2pi)/(3)+cos^(-1)((x-2)/(2))`

D

None of these

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

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

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

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

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

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

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

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

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

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

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

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  15. Let A={1,2,3,4,5} and functions f:A to and g: A to A to defined by f(1...

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  16. Suppose that f is an even function, g is an odd function and both f an...

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  17. If f(x)=e^(x) and g(x)= log(e)x, hen which of the following is true?

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  18. The inverse of the function f(x)=(e^x-e^(-x))/(e^x+e^(-x))+2 is given ...

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  19. Show that if f: R-{7/5}->R-{3/5} is defined by f(x)=(3x+4)/(5x-7) a...

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  20. Let f:R to be defined by f(x)=3x^(2)-5 and g : R to R by g(x)=(x)/(x^...

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