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`f: R^(+) to R` defined by `f(x) = log_(e)x, x in (0,1), f(x) =2 log_(e) x, x in [1, infty)` is

A

onto

B

one-one

C

not one-one but onto

D

a bijection

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The correct Answer is:
D
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
  1. The function f: R to R defined by f(x) =x-[x], AA x in R is

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  2. f: R^(+) to R defined by f(x) =2^(x) , x in (0,1), f(x) =3^(x), x in [...

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  3. f: R^(+) to R defined by f(x) = log(e)x, x in (0,1), f(x) =2 log(e) x,...

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  4. Statement -I: f: A to B is one -one and g: B to C is a one-one functio...

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  5. Observe the following Lists: Then the match for List -1 from Lis...

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  6. If f(x) =(e^(x) + e^(-x))/2, then the inverse function of f(x) is:

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  7. If f(x) =(10^(x)-10^(-x))/(10^(x) +10^(-x)) then f^(-1)(x)=

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  8. Let f: [1/2, 1] to [-1,1] is given by f(x) =4x^(3)-3x and f^(-)(x) is ...

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  9. The domain fo f(x)=(1)/(|sinx|+sinx) is

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  10. The domain of the function: f(x) =(tan 2x)/(6 cos x + 2 sin 2x) is:

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  11. The domain of the function f(x) = sqrt("cosec"x-1) is:

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  12. If f(x)=|sinx| has an inverse if its domain is

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  13. Domain of sin^(-1) 5x is:

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  14. The doamin of sqrt(1-3x)+Cos^(-1).(3x-1)/(2) is

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  15. Domain of Cos^(-1)sqrt(3x) is

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  16. The domain of the function f(x) =sqrt(sin^(-1)x) is:

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  17. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

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  18. The domain of sin^(-1)[(3x-1)/2] + sqrt(cos(sin x)) is:

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  19. The domain of the function: f(x) = sqrt(sin^(-1)(log(2)x)) + sin^(-...

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  20. The domain of f(x)=("cosec"^(-1)x)/([x]) is

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