Question 1170187
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Here is a general way to decompose a function into the composition of more than one function.<br>
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
(1) take the square root;
(2) multiply by -1; and 
(3) raise e to that power<br>
Since there are three operations, you could write the given function as the composition of three separate non-trivial functions.<br>
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:<br>
(a) combine steps (1) and (2):
(1) take the square root and multiply by -1; and
(2) raise e to that power<br>
The resulting decomposition is<br>
{{{g(x) = -sqrt(x)}}}
{{{f(x) = e^x}}}<br>
OR...<br>
(b) combine steps (2) and (3):
(1) take the square root; and
(2) multiply by -1 and raise e to that power<br>
The resulting decomposition is<br>
{{{g(x) = sqrt(x)}}}
{{{f(x) = e^(-x)}}}<br>