The composite mapping fog of the maps `f:R to R , f(x)=sin x and g:R to R, g(x)=x^(2)`, is

Options

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

Explanation

To find the composite mapping \( f \circ g \) of the functions \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = \sin x \) and \( g: \mathbb{R} \to \mathbb{R} \) defined by \( g(x) = x^2 \), we will follow these steps:

### Step 1: Understand the Functions
We have two functions:
- \( f(x) = \sin x \)
- \( g(x) = x^2 \)

### Step 2: Determine the Composite Function
The composite function \( f \circ g \) means we will substitute \( g(x) \) into \( f(x) \). This can be expressed as:
\[ f(g(x)) \]

### Step 3: Substitute \( g(x) \) into \( f(x) \)
Now we substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = f(x^2) \]
Since \( f(x) = \sin x \), we replace \( x \) with \( x^2 \):
\[ f(x^2) = \sin(x^2) \]

### Step 4: Write the Final Result
Thus, the composite mapping \( f \circ g \) is:
\[ f \circ g = \sin(x^2) \]

### Conclusion
The composite mapping \( f \circ g \) is \( \sin(x^2) \).

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