# How do you find (fog)(10) given f(x)=-9x-9 and g(x)=sqrt(x-9)?

Apr 12, 2017

$\textcolor{red}{- 18}$

#### Explanation:

$\left(f o g\right) \left(x\right)$ basically means $f \left(g \left(x\right)\right)$ $i . e .$ a function obtained by substituting $g \left(x\right)$ in place of $x$ in $f \left(x\right)$.

hence in this case,

$\left(f o g\right) \left(x\right) = f \left(g \left(x\right)\right) = - 9 \cdot g \left(x\right) - 9$
$= - 9 \cdot \sqrt{x - 9} - 9 = - 9 \sqrt{x - 9} - 9$

$\therefore$ $\left(f o g\right) \left(10\right) = f \left(g \left(10\right)\right) = - 9 \sqrt{10 - 9} - 9$
$= - 9 \cdot 1 - 9 = - 9 - 9 = \textcolor{red}{- 18}$

Another way to do it would have been to first find $g \left(10\right)$ ant then substitute the value obtained into $f \left(x\right)$.
$\therefore$ $g \left(10\right) = \sqrt{10 - 9} = \textcolor{red}{1}$
$\therefore$ $f \left(1\right) = - 9 \cdot 1 - 9 = 9 - 9 = \textcolor{red}{- 18}$