If gfx-sin x- and fgx-sin x 2- thenA- fx-sin 2 x- gx-xB- fx-sin x- gx-x-C- f x - x 2- g x -sin xD- f and g cannot be determined

If nbsp; f(x)=sin2x, nbsp;g(x)=x.f(g(x))=f(x)=sin2xg(f(x))=g(f(x))=g(sin2x)=sin2x=sin nbsp;xIf nbsp;f(x)=sin nbsp;x, nbsp;g(x)=|x|f(g(x))=f(|x|)=sin ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

If gfx=|sin x...

Question

If $g (f (x)) = ∣ ∣ sin x ∣ ∣ and f (g (x)) = {(sin \sqrt{x})}^{2}$ , then

f (x) = {sin}^{2} x, g (x) = \sqrt{x}

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f (x) = sin x, g (x) = | x |

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f (x) = x^{2}, g (x) = sin \sqrt{x}

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f and g cannot be determined

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Solution

The correct option is A $f (x) = {sin}^{2} x, g (x) = \sqrt{x}$
If
$f (x) = {sin}^{2} x, g (x) = \sqrt{x} . f (g (x)) = f (\sqrt{x}) = {sin}^{2} \sqrt{x} g (f (x)) = g (f (x)) = g ({sin}^{2} x) = \sqrt{{sin}^{2} x} = (sin x | If f (x) = sin x, g (x) = ∣ ∣ x ∣ ∣ f (g (x)) = f (∣ ∣ x ∣ ∣) = sin ∣ ∣ x ∣ ∣ \neq {(sin \sqrt{x})}^{2} If f (x) = x^{2}, g (x) = sin \sqrt{x} f (g (x)) = f (sin \sqrt{x}) = {(sin \sqrt{x})}^{2} g (f (x)) = g (x^{2}) = sin \sqrt{x^{2}} = sin ∣ ∣ x ∣ ∣ \neq (sin x |$

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