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.