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The image contains a problem regarding composition of functions. It states the following:

Given:
- \( f(x) = x^2 \)
- \( g(x) = x - 1 \)

The task is to find \( g(f(x)) \).

To solve this:

1. Start with \( f(x) = x^2 \).
2. Now, substitute \( f(x) \) into \( g(x) \). This means replacing \( x \) in \( g(x) = x - 1 \) with \( f(x) = x^2 \).
   
Thus:
\[
g(f(x)) = g(x^2) = x^2 - 1
\]

So, the complete expression is:
\[
g(f(x)) = x^2 - 1
\]

Would you like further clarification on this? Here are 5 related questions for further practice:

1. What is the composition of \( f(g(x)) \) for the same functions \( f(x) \) and \( g(x) \)?
2. If \( f(x) = 3x + 2 \) and \( g(x) = 2x - 5 \), what is \( g(f(x)) \)?
3. How do you find the inverse of a function, and what is the inverse of \( g(x) = x - 1 \)?
4. What are the domain and range of the composed function \( g(f(x)) \)?
5. How do we differentiate the composite function \( g(f(x)) \)?

**Tip**: When composing functions, always substitute the entire function inside the variable of the other function, treating it as a replacement for the variable.

If f(x) = x^2 and g(x) = x - 1, find g(f(x)).

This page explains how to solve the composition of functions g(f(x)) given f(x) = x^2 and g(x) = x - 1. Learn the step-by-step process, key algebraic concepts, and formulas involved. Suitable for students in Grades 9-10.

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