# Let f(x)=x^2 and g(x)=x+6, find: (f ∘ g) (x)?

Feb 27, 2018

$\left(f \circ g\right) \left(x\right) = {x}^{2} + 12 x + 36$

#### Explanation:

In this function composition, $\left(f \circ g\right) \left(x\right)$ indicates we are to put the $g$ function into the $f$ function as an input. Therefore, we are really looking for:

$f \left(\textcolor{red}{g} \left(x\right)\right) = {\left(\textcolor{red}{g} \left(x\right)\right)}^{2}$

Substituting, we get

$f \left(x + 6\right) = {\left(x + 6\right)}^{2}$

And finally expanding, our final answer is

$\left(f \circ g\right) \left(x\right) = {x}^{2} + 12 x + 36$