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Numerade Educator

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Problem 43 Medium Difficulty

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

$ F(x) = (2x + x^2)^4 $

Answer

$$\text { Let } g(x)=2 x+x^{2} \text { and } f(x)=x^{4} \text { . Then }(f \circ g)(x)=f(g(x))=f\left(2 x+x^{2}\right)=\left(2 x+x^{2}\right)^{4}=F(x)$$.

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Video Transcript

here we have capital f of X, and we're told to think of capital F of X as the composition F of G and another way to write that is, using parentheses f of G of X that shows us that G is going to be the inside function and f is going to be the outside function. Now there are different ways we could make this work. But the most obvious way is if we let the inside function B two X plus X squared. So we're gonna let G equal two x plus X squared. Now what would the outside function be? Well, what are we doing to that thing? We're raising it to the fourth. We'll just call that thing X. So that means that G of X is two x plus x squared and f of X, his X to the fourth power. And when you put G inside f, you get capital F