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))`

Answer

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

### Step 1: Understand the composition of functions
The composite function \( f \circ g \) means that we will apply the function \( g \) first and then apply the function \( f \) to the result of \( g \).

### Step 2: Write down the functions
We have:
- \( f(x) = \sin x \)
- \( g(x) = x^2 \)

### Step 3: Substitute \( g(x) \) into \( f \)
To find \( f \circ g \), we need to compute \( f(g(x)) \):
\[ f(g(x)) = f(x^2) \]

### Step 4: Replace \( x \) in \( f(x) \) with \( g(x) \)
Now we substitute \( g(x) = x^2 \) into \( f(x) = \sin x \):
\[ f(x^2) = \sin(x^2) \]

### Step 5: 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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