## Function Machines

\[f(x)=2x^2-3\]

\[f\]

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

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

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

.