# How do you find (fog)(x) given f(x)=x^2+7 and g(x)=x-3?

Mar 26, 2017

$\left(f o g\right) \left(x\right)$ can be written as $f \left(g \left(x\right)\right)$. I prefer the latter notation, because it better illustrates that you substitute the equivalent of $g \left(x\right)$ for every x that you see in $f \left(x\right)$.

#### Explanation:

Given: $f \left(x\right) = {x}^{2} + 7$ and $g \left(x\right) = x - 3$

To find $f \left(g \left(x\right)\right)$, we substitute $x - 3$ for every x that we see in $f \left(x\right)$:

$f \left(g \left(x\right)\right) = {\left(x - 3\right)}^{2} + 7$

Technically, we are done but it is better to simplify the right side:

$f \left(g \left(x\right)\right) = {x}^{2} - 6 x + 9 + 7$

$f \left(g \left(x\right)\right) = {x}^{2} - 6 x + 16 \leftarrow$ the answer