If function `f:RtoR` is defined by `f(x)=sinx` and function `g:RtoR` is defined by `g(x)=x^(2),` then (fog)(x) is

Options

A. `x^(2)sinx`
B. `(sinx)^(2)`
C. `sinx^(2)`
D. `(sinx)/(x^(2))`

Answer

To solve the problem, we need to find the composition of the two functions \( f \) and \( g \), denoted as \( (f \circ g)(x) \).

1. **Identify the functions**:
- We have \( f(x) = \sin x \)
- We have \( g(x) = x^2 \)

2. **Write the composition**:
- The composition \( (f \circ g)(x) \) means we need to substitute \( g(x) \) into \( f(x) \).
- This can be expressed as \( (f \circ g)(x) = f(g(x)) \).

3. **Substitute \( g(x) \) into \( f(x) \)**:
- We know \( g(x) = x^2 \), so we substitute this into \( f \):
\[ f(g(x)) = f(x^2) \]

4. **Evaluate \( f(x^2) \)**:
- Since \( f(x) = \sin x \), we replace \( x \) with \( x^2 \):
\[ f(x^2) = \sin(x^2) \]

5. **Final result**:
- Therefore, the composition \( (f \circ g)(x) \) is:
\[ (f \circ g)(x) = \sin(x^2) \]

### Summary of the Solution:
The final answer is:
\[ (f \circ g)(x) = \sin(x^2) \]