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\n" ); document.write( "Here is a general way to decompose a function into the composition of more than one function.
\n" ); document.write( "First, make an ordered list of the operations performed on the input value by the function. (That is, imagine the steps you would do to evaluate the function for a given input). In this example, the operations are
\n" ); document.write( "(1) take the square root;
\n" ); document.write( "(2) multiply by -1; and
\n" ); document.write( "(3) raise e to that power
\n" ); document.write( "Since there are three operations, you could write the given function as the composition of three separate non-trivial functions.
\n" ); document.write( "To write the given function as the composition of two functions, combine two of the three steps into one. There are clearly two different ways you could do this:
\n" ); document.write( "(a) combine steps (1) and (2):
\n" ); document.write( "(1) take the square root and multiply by -1; and
\n" ); document.write( "(2) raise e to that power
\n" ); document.write( "The resulting decomposition is
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\n" ); document.write( "OR...
\n" ); document.write( "(b) combine steps (2) and (3):
\n" ); document.write( "(1) take the square root; and
\n" ); document.write( "(2) multiply by -1 and raise e to that power
\n" ); document.write( "The resulting decomposition is
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