Given the function \( g(x) = 5x - 7 \), you need to find \( g(x^2 + 1) \).

### Step-by-Step Solution:

1. **Substitute \( x^2 + 1 \) into the function**:
   \[
   g(x^2 + 1) = 5(x^2 + 1) - 7
   \]

2. **Distribute the 5**:
   \[
   g(x^2 + 1) = 5x^2 + 5 - 7
   \]

3. **Simplify the expression**:
   \[
   g(x^2 + 1) = 5x^2 - 2
   \]

So, the final answer is:
\[
g(x^2 + 1) = 5x^2 - 2
\]

Would you like further details or have any questions about this process?

### Related Questions:
1. What is the value of \( g(3) \) using the given function \( g(x) = 5x - 7 \)?
2. How would you find \( g(a + b) \) for any \( a \) and \( b \)?
3. If \( h(x) = 2x^2 + 3x + 1 \), how would you compute \( h(x + 1) \)?
4. What is the inverse of the function \( g(x) = 5x - 7 \)?
5. How do you graph the function \( g(x) = 5x - 7 \)?
6. What is the range of the function \( g(x) = 5x - 7 \)?
7. How would you find the derivative of \( g(x) = 5x - 7 \) if it were a continuous function?
8. If \( g(x) = 5x - 7 \), what is \( g(2x) \)?

### Tip:
When substituting expressions into a function, ensure that you distribute and simplify correctly to avoid errors in the final expression.

Learn how to find g(x^2 + 1) using the function g(x) = 5x - 7. Step-by-step solution provided with detailed substitution and simplification. Suitable for students in Grades 7-9.

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