𝑔(𝑥) = 5𝑥 − 7 ; 𝑓𝑖𝑛𝑑 𝑔(𝑥 2 + 1)

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

Would you like to explore this further or need more explanations?

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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.

Learn how to evaluate g(x^2 + 1) using the function g(x) = 5x - 7. This problem demonstrates function evaluation at composite expressions, substitution techniques, and linear function properties. Suitable for high school students.

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