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If $f : R \to R, g : R \to R$ be two functions given by $f (x) = 2 x - 3, g (x) = x^{3} + 5$ . Then, ${(fog)}^{- 1} (x)$ is equal to

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x+721/3

x-721/3

x-271/3

x-721/3

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detailed solution

Correct option is D

f:R→R g:R→R f(x)=2x-3 g(x)=x3+5 ⇒ (fog)(x)=f(g(x))=f(x3+5)=2(x3+5)-3 =2x3+7Now, let let y=2x3+7 2x3=y-7 x=y-721/3 Replacing x by y, we get y=x-721/3 ∴ (fog)-1(x)=x-721/3

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If f:R→R, g :R→R be two functions given by f(x)=2x-3, g(x)=x3+5. Then,fog-1(x) is equal to

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If $f : R \to R, g : R \to R$ be two functions given by $f (x) = 2 x - 3, g (x) = x^{3} + 5$ . Then, ${(fog)}^{- 1} (x)$ is equal to