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If f'(x^2-4x+3)gt0 " for all " x in (2,...

If `f'(x^2-4x+3)gt0 " for all " x in (2,3) `then f(sinx) is increasing on

A

`bigcup underset(n epsilon I)(2npi,(4n+1)pi//2)`

B

R

C

`bigcup underset(n epsilon I)((4n-1)pi//2,2 n pi)`

D

None of theese

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Verified by Experts

The correct Answer is:
3
`2lt xlt 3 rArr -1 lt x^(2)-4x+3 lt 0`
`therefore f'(x)gt 0 for -21 lt xlt 0`
`therefore f(x)uparrow`
`f(sin x)uparrow if -1 lt sin x lt 0`
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