Find fog and gof if:
`f(x)=sinx,g(x)=x^(2)`

Explanation

To find \( f \circ g \) and \( g \circ f \) for the functions \( f(x) = \sin x \) and \( g(x) = x^2 \), we will follow these steps:

### Step-by-Step Solution

1. **Define the Functions**:
- We have \( f(x) = \sin x \) and \( g(x) = x^2 \).

2. **Find \( f \circ g \)**:
- The composition \( f \circ g \) means we need to evaluate \( f(g(x)) \).
- Substitute \( g(x) \) into \( f \):
\[ f(g(x)) = f(x^2) = \sin(x^2) \]
- Therefore, \( f \circ g = \sin(x^2) \).

3. **Find \( g \circ f \)**:
- The composition \( g \circ f \) means we need to evaluate \( g(f(x)) \).
- Substitute \( f(x) \) into \( g \):
\[ g(f(x)) = g(\sin x) = (\sin x)^2 \]
- Therefore, \( g \circ f = \sin^2 x \).

4. **Summary of Results**:
- \( f \circ g = \sin(x^2) \)
- \( g \circ f = \sin^2 x \)