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Numerade Educator

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Problem 46 Medium Difficulty

Express the function in the form $ f \circ g $.

$ G(x) = \sqrt[3]{\dfrac {x}{1 + x}} $

Answer

$f(x)=\sqrt[3]{x}$
$g(x)=\frac{x}{x+1}$

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Video Transcript

all right here we have capital G of X, and we want to think of G of X as a composition of F of G. Another way to write that is with parentheses. F of g of X. So from that we can see that G is the inside function and F is the outside function and there are actually many different ways. We could do this problem correctly. We'll just go over the most obvious one. So the inside function could be what we see inside this cube root sign so we could let g of x b the quotient X over one plus X. And if that's the case, then what's the outside? The outside would be the cube root function, so the outside function F of X would be the cube root of X.