If `f(x)=10x-7 and (fog)(x)=x`, then `g(x)` is equal to:

Options

A. `(x+7)/(10)`
B. `(x-7)/(10)`
C. `(1)/(10x-7)`
D. None of these

Answer

To solve the problem, we need to find the function \( g(x) \) given that \( f(x) = 10x - 7 \) and \( (f \circ g)(x) = x \).

### Step-by-step Solution:

1. **Understand the Composition of Functions**:
We know that \( (f \circ g)(x) = f(g(x)) \). According to the problem, this is equal to \( x \).

2. **Substitute the Function**:
We can express this as:
\[ f(g(x)) = x \]
Given \( f(x) = 10x - 7 \), we can replace \( f \) with its expression:
\[ 10g(x) - 7 = x \]

3. **Rearrange the Equation**:
To isolate \( g(x) \), we first add 7 to both sides:
\[ 10g(x) = x + 7 \]

4. **Solve for \( g(x) \)**:
Now, divide both sides by 10:
\[ g(x) = \frac{x + 7}{10} \]

Thus, the function \( g(x) \) is:
\[ \boxed{g(x) = \frac{x + 7}{10}} \]