Find gof if `f(x)= 8x-2` and `g(x) = 2x`

Explanation

To find \( g \circ f \) (denoted as \( g(f(x)) \)), we will follow these steps:

1. **Identify the functions**: We have two functions given:
- \( f(x) = 8x - 2 \)
- \( g(x) = 2x \)

2. **Understand the composition**: The notation \( g \circ f \) means we need to substitute \( f(x) \) into \( g(x) \). This can be expressed as:
\[ g(f(x)) = g(8x - 2) \]

3. **Substitute \( f(x) \) into \( g(x) \)**: Now we will replace \( x \) in \( g(x) \) with \( f(x) \):
\[ g(8x - 2) = 2(8x - 2) \]

4. **Simplify the expression**: Now we will simplify the expression:
\[ g(8x - 2) = 2 \times 8x - 2 \times 2 = 16x - 4 \]

5. **Final result**: Therefore, the composition \( g \circ f \) is:
\[ g \circ f = 16x - 4 \]

### Summary of the Steps:
1. Identify the functions \( f(x) \) and \( g(x) \).
2. Understand that \( g(f(x)) \) means substituting \( f(x) \) into \( g(x) \).
3. Substitute \( f(x) \) into \( g(x) \).
4. Simplify the resulting expression.
5. State the final result.