# If f(x)=3x² and g(x)=4-5x, how do you calculate f(g(10))?

May 29, 2016

6348

#### Explanation:

Note: Names such as $f \left(x\right) , g \left(x\right) , h \left(x\right) \text{ and so on }$are just a way of identifying some sort of mathematical equation structure or process.
If you like, it is a bit like it is a bit like a mathematical machine that has a name.

So $g \left(10\right)$ means that you put the value of 10 into the machine $g \left(x\right)$ and it applies $4 = \left(5 \times 10\right)$ to that value of 10. so the 'machine' $g \left(x\right)$ outputs

$\textcolor{b r o w n}{g \left(x\right) = 4 - 5 x} \textcolor{b l u e}{\text{ "->" } g \left(10\right) = 4 - \left(5 \times 10\right) = - 46}$

Now that we have that output we have:

$f \left(g \left(10\right)\right) \to f \left(- 46\right)$

color(brown)(f(x)=3x^2)color(blue)(" "->" "f(-46)=3xx(-46)^2= 6348