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Let f(x) = sinx and g(x) = log|x|.If the...

Let f(x) = sinx and `g(x) = log|x|`.If the ranges of composite functions fog and gof are `R_1` and `R_2` repsectively, then

A

`R_(1)={u:-1 le u le 1}, R_(2)={v: -infty lt v lt 0}`

B

`R_(1) ={u: - infty lt u le 0}, R_(2)={u:-1 le u le 1}`

C

`R_(3)={u:-1 lt u lt 1}, R_(2)={v: - infty lt v lt 0}`

D

`R_(1) ={u:-1 le u le 1}, R_(2)={v:-infty lt v le 0}`

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
  1. If f : R to R is defined by f(x) = [2x]-2[x] for x in R, where [x] is...

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  2. The range of sin log [(sqrt(4-x^(2))/(1-x))] is

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  3. Let f(x) = sinx and g(x) = log|x|.If the ranges of composite functions...

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  4. If f from [-1,1] into [-1,1] defined by f(x) =3x-5 then f is:

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  5. If f: D to R be the function with domain: D={x: -pi/2 lt x lt pi/2} ...

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  6. If f: R to R defined by f(x) ={{:(2x+5, if, x gt 0),(3x-2, if, x le 0...

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  7. If f: R to R is defined by f(x) =x+ sqrt(x^(2)), then f is:

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  8. A={x:-1 le x le 1}, f: A to A defined by f(x) =x|x|. Then f is:

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  9. If f(x)=|x-1|+|x-2|+|x-3|,2 lt x lt 3, then f is

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  10. y=f(x) =x/(1+|x|), x in R, y in R is

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  11. f: R to R is a function defined by f(x) =(e^(|x|) -e^(-x))/(e^(x) + e^...

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  12. If f: R to R defined by f(x) =(e^(x^(2)) -e^(-x^(2)))/(e^(x^(2)) +e^(-...

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  13. If f:[0,1] to [-1,3] defined by f(x) =x^(2)+x+1, then f is

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  14. If f: R to R defined by f(x) =x^(2)-2x-3, then f is:

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  15. If f:R rarr(0, 1] is defined by f(x)=(1)/(x^(2)+1), then f is

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  16. If f: R to R is defined by f(x)=(x^(2)-4)/(x^(2)+1), then f(x) is

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  17. Which of the following functions is not injective ?

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  18. The function f: R to R defined by f(x) =x-[x], AA x in R is

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

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  20. 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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