∫$$dx2$$−$$3x$$−$$x2=(fog)$$⁡$$(x)+C$$ then

Correct option is 3f(x)=sin−1⁡x,g(x)=2x+317

Questions

$\int \frac{d x}{\sqrt{2 - 3 x - x^{2}}} = (fog) (x) + C$ then

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f(x)=sin−1⁡x,g(x)=2x−317

∫(x)=tan−1⁡x,g(x)=2x+317

f(x)=sin−1⁡x,g(x)=2x+317

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detailed solution

Correct option is C

∫dx2−3x−x2=∫dx−x2+3x−2=∫dx−(x+3/2)2−17/4=∫dx17/4−(x+3/2)2=sin−1⁡x+3/217/4+C=sin−1⁡2x+317+CTherefore g(x)=2x+317 and f(x)=sin−1⁡x

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∫dx2−3x−x2=(fog)⁡(x)+C then

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$\int \frac{d x}{\sqrt{2 - 3 x - x^{2}}} = (fog) (x) + C$ then