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Let f(x) =1+2sin(e^x/(e^x+1)) x ge 0 the...

Let `f(x) =1+2sin(e^x/(e^x+1))` `x ge 0` then `f^(-1)(x) ` is equal to (assuming f is bijectve)

A

`log ((sin^(-1)((x-1)/2))/(1 - sin^(-1) (( x-1)/2))) `

B

`log ((sin (( x-1)/2))/(1- sin((x-1)/2)))`

C

`e^((sin^(-1).((x-1)/2))/(1-sin^(-1)((x-1)/2)))`

D

`e^((sin((x-1)/2))/(1-sin ((x-1)/2)))`

Text Solution

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The correct Answer is:
A
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ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single Option Correct Type Questions)
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  2. The equation e^(sin^(-1)x)/pi=y/(log y) has

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  3. Let f(x) =1+2sin(e^x/(e^x+1)) x ge 0 then f^(-1)(x) is equal to (assu...

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  4. cos^(-1) (cos (2 cot^(-1) (sqrt2 -1))) is equal to

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  5. The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is

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  6. If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=tan2^0 (b) x=tan4^0 x=tan1/4...

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  7. If tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2, then ...

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  8. The number of solution of the equation |tan^(-1)|x||=sqrt((x^(2)+1)^(2...

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  9. For any real number x ge 1, the expression sec^(2)x ( tan^(-1)x) - ...

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  10. Let f : R to [0, pi/2) be defined by f ( x) = tan^(-1) ( x^(2) + x +...

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  11. The value of expression tan^(- 1)((sqrt(2))/2)+sin^(- 1)((sqrt(5))/5)-...

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  12. The value of sec ( 2 cot^(-1) 2 + cos^(-1) . 3/5) is equal to

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  13. Which one of the following statement is meaningless ?

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  14. The value of sec(sin^-1(sin((-50pi)/9))+cos^-1(cos(31pi)/9))

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  15. The number k is such that tan { arc tan (2) + arc tan (20 k) } = k. ...

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  16. The value of Sigma( r =1)^( infty) tan^(-1) ( 1/( r^(2) - 5r + 7)) ,...

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  17. If x = tan^(-1) 1 - cos^(-1) ( - 1/2) + sin^(-1) 1/2 , y = cos (1/2 c...

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  18. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A)=0

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  19. Prove that : tan^-1(1/2) + tan^-1(1/5) + tan^-1(1/8) = pi/4

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  20. Number of solutions (s) of the equations cos^(-1) ( 1-x) - 2 cos^(-...

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