If `g(x-3)=5x+1` for all values of x, what is the value of `g(-2)`?

Answer

To find the value of \( g(-2) \) given that \( g(x-3) = 5x + 1 \), we can follow these steps:

### Step 1: Set up the equation
We start with the equation provided:
\[ g(x-3) = 5x + 1 \]

### Step 2: Identify the value of \( x \)
To find \( g(-2) \), we need to determine what value of \( x \) will make \( x - 3 = -2 \). We can set up the equation:
\[ x - 3 = -2 \]

### Step 3: Solve for \( x \)
Now, we solve for \( x \):
\[ x = -2 + 3 \]
\[ x = 1 \]

### Step 4: Substitute \( x \) back into the equation
Now that we have \( x = 1 \), we can substitute this value back into the original equation to find \( g(-2) \):
\[ g(-2) = g(1 - 3) = 5(1) + 1 \]

### Step 5: Calculate the right-hand side
Now we calculate the right-hand side:
\[ g(-2) = 5 \cdot 1 + 1 = 5 + 1 = 6 \]

### Conclusion
Thus, the value of \( g(-2) \) is:
\[ \boxed{6} \]