Question

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

Answer 1

6348

Explanation:

Note: Names such as `f(x) ,g(x), h(x) " 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(10)` means that you put the value of 10 into the machine `g(x)` and it applies `4=(5xx10)` to that value of 10. so the 'machine' `g(x)` outputs

`color(brown)(g(x)=4-5x)color(blue)(" "->" "g(10)=4-(5xx10) = -46)`

Now that we have that output we have:

`f(g(10)) ->f(-46)`

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