Question

Express the following function, F(x) as a composition of two functions f and g. F(x)= x^2/(x^2 + 4)

Answer 1

There are many solutions for f and g.
Here is one solution:
\[F(x) = \frac{ x ^{2} }{ (x ^{2} + 4)}\]
\[g(x) = x ^{2}\] and \[f(x) = \frac{ x }{(x + 4) }\]
So F(x) = (f o g)(x)

Answer 2

Would I write f(x) (f o g)(x) as my answer or include the x^2 and x/(x+4) too so it shows my reasoning?

Answer 3

You can write the answer as:
g(x) = x^2
f(x) = x / (x + 4)
F(x) = (f o g)(x) = x^2 / (x^2 + 4)

Answer 4

Don't forget the original function is upper case F and the two functions are lower case f and g as the problem states.

Answer 5

Right. Ok, seriously thank you. Hopefully I do well on this upcoming test

Answer 6

Best Wishes!