# Let f(x) = 7x^2+5 and g(x) = x-3, how do you find the composite function (f o g)(x)?

$f \left(g \left(x\right)\right) = 7 {x}^{2} - 42 x + 68$
To find a composite function, you simply insert $g \left(x\right)$ into $f \left(x\right)$ anywhere you would find the $x$ variable:
$f \left(g \left(x\right)\right) = 7 {\left(x - 3\right)}^{2} + 5$
$= 7 \left({x}^{2} - 6 x + 9\right) + 5$
$= 7 {x}^{2} - 42 x + 63 + 5$
$= 7 {x}^{2} - 42 x + 68$