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f(x)=sin^(-1)[e^(x)]+sin^(-1)[e^(-x)] wh...

`f(x)=sin^(-1)[e^(x)]+sin^(-1)[e^(-x)]` where [.] greatest integer function then
a. domain of `f(x) = (-"In 2, In 2")`
b. range of f(x) = `{pi}`
c. f(x) has removable discontinuity at x = 0
d. `f(x) = cos^(-1) x` has only solution

A

domain of `f(x) = (-"In 2, In 2")`

B

range of f(x) = `{pi}`

C

f(x) has removable discontinuity at x = 0

D

`f(x) = cos^(-1) x` has only solution

Text Solution

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The correct Answer is:
A, C
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. For every pair of continuous function f, g : [0, 1] rarr R such that m...

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  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

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  5. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

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  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

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  7. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

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  11. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

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  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

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  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

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  17. Which of the following functions is differentiable at x = 0 ?

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  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

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  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

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  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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