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  4. If g(x)=1+√[3]x then a function f such that f(g(x))=3-3(√[3]x)+x is

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Q. If $g(x)=1+\sqrt[3]{x}$ then a function $f$ such that $f(g(x))=3-3(\sqrt[3]{x})+x$ is

Relations and Functions - Part 2

Solution:

Let $g(x)=1+\sqrt[3]{x}=y \Rightarrow x^{1 / 3}=y-1$
$\text { so } f(g(x))=3-3 x^{1 / 3}+x$
$\Rightarrow f(y)=3-3(y-1)+(y-1)^3 $
$=y^3-3 y^2+5$