To find gofx and fogx, we start by understanding what these notations mean. Here, gofx means we need to substitute fx into g, and fogx means we substitute gx into f.
First, let’s find gofx:
- Given that fx = sin x, we need to find g(sin x).
- Since g(x) = cos x, we replace x with sin x.
- Thus, gofx = g(sin x) = cos(sin x).
Now, let’s calculate fogx:
- Here, we need to find f(gx) where gx = cos x.
- Since f(x) = sin x, we replace x with cos x.
- Therefore, fogx = f(cos x) = sin(cos x).
In conclusion, we have:
- gofx = cos(sin x)
- fogx = sin(cos x)