To find $g(x^2 + 1)$ for the given function $g(x) = 5x - 7$, we need to substitute $x^2 + 1$ into the function $g(x)$.

The function $g(x)$ is given as:

$g(x) = 5x - 7$

Substitute $x^2 + 1$ for $x$ in the function:

$g(x^2 + 1) = 5(x^2 + 1) - 7$

Now, distribute the 5:

$g(x^2 + 1) = 5x^2 + 5 - 7$

Finally, simplify the expression:

$g(x^2 + 1) = 5x^2 - 2$

So, $g(x^2 + 1) = 5x^2 - 2$.

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Here are 8 related questions you might find useful:

1. How do you evaluate functions at composite expressions like $g(x^2 + 1)$?
2. What is the general form of a linear function?
3. How do you find the inverse of the function $g(x) = 5x - 7$?
4. What is the effect of substituting a quadratic expression into a linear function?
5. How would you evaluate $g(x^2 - 1)$ for the same function $g(x) = 5x - 7$?
6. Can you graph the function $g(x^2 + 1)$?
7. How do you find the roots of $g(x^2 + 1) = 0$?
8. How do you determine the range of the function $g(x^2 + 1)$?

Tip: When substituting expressions into functions, ensure each part is simplified correctly before combining like terms.