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 1: Find \( f \circ g \)

The composition \( f \circ g \) is defined as \( f(g(x)) \).

1. Start with the function \( g(x) = x^2 \).
2. Substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = f(x^2) \]
3. Now, apply the function \( f \):
\[ f(x^2) = \sin(x^2) \]

Thus, we have:
\[ f \circ g = \sin(x^2) \]

### Step 2: Find \( g \circ f \)

The composition \( g \circ f \) is defined as \( g(f(x)) \).

1. Start with the function \( f(x) = \sin x \).
2. Substitute \( f(x) \) into \( g(x) \):
\[ g(f(x)) = g(\sin x) \]
3. Now, apply the function \( g \):
\[ g(\sin x) = (\sin x)^2 \]

Thus, we have:
\[ g \circ f = (\sin x)^2 \]

### Final Answers:
- \( f \circ g = \sin(x^2) \)
- \( g \circ f = (\sin x)^2 \)

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