# (f○g)(x)=√(1-3x²)/(2x-8) and (g○f)(x)=(1-3x²)/(3-2x²) . How to find f(g(4))?

Jul 15, 2015

$\left(f \circ g\right) \left(x\right)$ is an alternate way of writing $f \left(g \left(x\right)\right)$ and is undefined when $x = 4$

#### Explanation:

$f \left(g \left(x\right)\right)$ is the same as $\left(f \circ g\right) \left(x\right)$

So
$f \left(g \left(4\right)\right)$ is the same as $\left(f \circ g\right) \left(4\right)$

But
$\left(f \circ g\right) \left(x\right) = \frac{\sqrt{1 - 3 {x}^{2}}}{2 x - 8}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$...or $\sqrt{\frac{1 - 3 {x}^{2}}{2 x - 8}}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$it's hard to guess the range of the root symbol
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$and doesn't make any difference in this case, since...
When $x = 4$
$\textcolor{w h i t e}{\text{XXXX}}$we have an attempt to divide by zero
$\textcolor{w h i t e}{\text{XXXX}}$which is undefined.