## 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.
$f(3x+2)$
, 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
$x^2+6 \gt (x-3)^2$

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