If f - x 2-4 x -3-0- - x -2-3- then f sin x is increasing onA- R B- -n - Z2 n -4 n-1 -2C- -n - Z4 n-1 - 2 n -D- - n - Z 4 n -1 -2- 2 n -

The correct option is D n ϵ Z∪ ((4n 1) π/2,2nπ )x ϵ (2, 3) ⇒ 1 lt; x^2 4x + 3 lt; 0, so f(x) is increasing in ( 1, 0) ⇒ f (sin x) is increasing on n ...

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Byju's Answer

Standard XII

Mathematics

Using Monotonicity to Find the Range of a Function

If f ' x 2-4 ...

Question

If f' $(x^{2} - 4 x + 3) > 0, \forall x ϵ (2, 3)$ ; then f (sin x) is increasing on

\cup n ϵ Z (2 n π, (4 n + 1) \frac{π}{2})

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\cup n ϵ Z ((4 n - 1) \frac{π}{2}, 2 n π)

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R

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\cup n ϵ Z ((4 n - 1) π, 2 n π)

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Solution

The correct option is B $\cup n ϵ Z ((4 n - 1) \frac{π}{2}, 2 n π)$
$x ϵ (2, 3) \Rightarrow - 1 < x^{2} - 4 x + 3 < 0$ , so f(x) is increasing in (-1, 0)
$\Rightarrow$ f (sin x) is increasing on $\cup n ϵ Z ((4 n - 1) \frac{π}{2}, 2 n π)$

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If f' (x2−4x+3)>0,∀xϵ(2,3); then f (sin x) is increasing on

The correct option is B ∪nϵZ((4n−1)π2,2nπ)xϵ(2,3)⇒−1<x2−4x+3<0, so f(x) is increasing in (-1, 0) ⇒ f (sin x) is increasing on ∪nϵZ((4n−1)π2,2nπ)

If f' $(x^{2} - 4 x + 3) > 0, \forall x ϵ (2, 3)$ ; then f (sin x) is increasing on

The correct option is B $\cup n ϵ Z ((4 n - 1) \frac{π}{2}, 2 n π)$
$x ϵ (2, 3) \Rightarrow - 1 < x^{2} - 4 x + 3 < 0$ , so f(x) is increasing in (-1, 0)
$\Rightarrow$ f (sin x) is increasing on $\cup n ϵ Z ((4 n - 1) \frac{π}{2}, 2 n π)$