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In some cases it is desirable to decompose a function to write it as a...

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Calculus

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In some cases it is desirable to decompose a function to write it as a composition of two simpler functions Example 13 Write f x 3 5 22 as the composition of two functions Show solution Solution We are looking for two functions g and h so f x g h z To do this we look for a function inside a function in the formula for f x As one possibility we might notice that 5 is the inside of the square root We could then decompose the function as h x 5 r g x 3 z We can check our answer by recomposing the functions g h z g 5 3 5 2 Note that this is not the only solution to the problem Another non trivial decomposition would be h x and g x 3 5 z Write f x 199 h x 10 Exercise 1 4 8 3 as the composition of two simpler functions f x g h x x 2 20

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