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 \( g(x) \) such that when we compose it with \( f(x) \), we get back \( x \). Given that \( f(x) = 10x - 7 \) and \( (f \circ g)(x) = x \), we can follow these steps:

### Step 1: Understand the composition of functions
The notation \( (f \circ g)(x) \) means \( f(g(x)) \). According to the problem, we have:
\[ f(g(x)) = x \]

### Step 2: Substitute \( g(x) \) into \( f(x) \)
Since \( f(x) = 10x - 7 \), we can write:
\[ f(g(x)) = 10g(x) - 7 \]

### Step 3: Set up the equation
From the composition, we know:
\[ 10g(x) - 7 = x \]

### Step 4: Solve for \( g(x) \)
To isolate \( g(x) \), we will first add 7 to both sides:
\[ 10g(x) = x + 7 \]
Now, divide both sides by 10:
\[ g(x) = \frac{x + 7}{10} \]

### Step 5: Conclusion
Thus, the function \( g(x) \) is:
\[ g(x) = \frac{x + 7}{10} \]