Let f : `R rarr R`, g : `R rarr R` be two functions given by f(x) = 2x - 3, g(x) `= x^(3) + 5`. Then `(fog)` (x) is equal to

Options

A. `((x+7)/(2))^(1//3)`
B. `(x - (7)/(2))^(1//3)`
C. `((x-2)/(7))^(1//3)`
D. `((x-7)/(2))^(1//3)`

Answer

To find \( (f \circ g)(x) \), which is the composition of the functions \( f \) and \( g \), we will follow these steps:

1. **Identify the Functions**: We have two functions defined as follows:
- \( f(x) = 2x - 3 \)
- \( g(x) = x^3 + 5 \)

2. **Substitute \( g(x) \) into \( f(x) \)**: We need to find \( f(g(x)) \). This means we will substitute \( g(x) \) into \( f(x) \).
\[ f(g(x)) = f(x^3 + 5) \]

3. **Apply the Function \( f \)**: Now we will apply the function \( f \) to \( g(x) \):
\[ f(g(x)) = f(x^3 + 5) = 2(x^3 + 5) - 3 \]

4. **Simplify the Expression**: We will simplify the expression obtained:
\[ = 2(x^3 + 5) - 3 = 2x^3 + 10 - 3 \]
\[ = 2x^3 + 7 \]

5. **Final Result**: Therefore, the composition \( (f \circ g)(x) \) is:
\[ (f \circ g)(x) = 2x^3 + 7 \]

### Final Answer:
\[ (f \circ g)(x) = 2x^3 + 7 \]