Verified answer

(f o g)(x) simply means to plug in g(x) as the input for f(x) so it can also be seen as f(g(x)).

Because of this f(x) and g(x) can be different functions, here are a few:

1. f(x) = 1/x

then g(x) = sin(x)^2

2. f(x) = 1/x^2

then g(x) = sin(x)

3. f(x) = x

then g(x) = 1/(sin(x)^2)

You can also make things more confusing but still correct so that (f o g)(x) = 1/(sin(x)^2)

4. f(x) = x^2

then g(x) = SQRT(1/(sin(x)^2))

Any of the above answers are correct, although it is easiest to choose a simple answer. Now remember if you are told what f(x) or g(x) is then you have to solve with that to make the (f o g)(x) equal to the final equation. Hope this helps!