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Function Machines

Just like a function, a function machine takes an argument computes a number.
\[f(x)=2x^2-3\]

\[f\]
  takes an argument, squares it, multiplies the anser by 2 and subtracts 3.
If instead we want  
\[f(3x+2)\]
, the function  
\[f\]
  will take  
\[3x+2\]
, square it, multiply the answer by 2 and subtract 3.
A function machine acts in the same way and we can use this to solve problems. Consider the function machines below.

Suppose the inputs are the same for each machine A and B. We want the set of values of input for which the output of machine A is greater than the output of machine B.
Let the input to each machine be  
\[x\]
.
The output from A is  
\[x^2+6\]

The output from B is  
\[(x-3)2\]

Then we require  
\[x^2+6 \gt (x-3)^2\]

\[x^2+6 \gt x^2-6x+9 \rightarrow 6x \gt -6x+9 \rightarrow 12x \gt 9 \rightarrow x \gt \frac{9}{12} =\frac{3}{4}\]
.

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