How do you write y = 3sqrt(1 + x^2) as a composition of two simpler functions?

2 Answers
Aug 11, 2015

Define these functions:
g(x)=1+x^2
f(x)=3sqrtx

Then:
y(x)=f(g(x))

Aug 13, 2015

There is more than one way to do this.

Explanation:

Adrian D has given one answer, here are two more:

Let g(x) be the first thing we do if we knew x and started to calculate:

g(x) = x^2" "

Now f will be the rest of the calculation we would do (after we found x^2)

It may be easier to think about if we gave g(x) a temporary name, say g(x)=u

So we see that y = 3sqrt(1+u)

So f(u) = 3sqrt(1+u) and that tells us we want:

f(x) = 3sqrt(1+x)

Another answer is to let f(x) be the last thing we would do in calculating y.

So let f(x) = 3x

To get y = f(g(x)) we need 3g(x) = y

So let g(x) = sqrt(1+x^2)