document.write( "Question 800690: Express the function y = 9 (x - 4)^{4} as a composition y = f(g(x)) of two simpler functions y = f(u) and u = g(x) \n" ); document.write( "

Algebra.Com's Answer #483195 by josgarithmetic(39618) $\"\"$ $\"About$

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Try to decompose the composition of y.\r
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\n" ); document.write( "\n" ); document.write( "Maybe assign $\"u=x-4\"$ . This can allow to say, $\"y=9u%5E4\"$ . The function that takes u as an input is $\"something%28t%29=9t%5E4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "u=g(x), and something(t) has been given g(x) as input, so you have like, $\"something%28g%28x%29%29=y\"$ . That was a name just used for planning. We can call \"something\", as f.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28g%28x%29%29\"$ is the composition f o g where $\"f%28x%29=9x%5E4\"$ and $\"g%28x%29=x-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "That may seem twisted to think through, but normally we start from the other direction in academic exercises, given functions, told something about the composition, and then form the composition and do something with one or the other or evaluate the composition at some value of x. \n" ); document.write( "

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