Iff (x) - 2x - 5 and g (x) = 1 - x}, then (g • f) (2) = 0.

You provided the functions:

- \( f(x) = 2x - 5 \)
- \( g(x) = 1 - x \)

You are asked to find \( (g \circ f)(2) \), which represents the composition of \( g(x) \) and \( f(x) \), and the result is given to be \( 0 \).

### Step-by-Step Solution:

1. **Find \( f(2) \):**
   \[
   f(x) = 2x - 5
   \]
   Substituting \( x = 2 \):
   \[
   f(2) = 2(2) - 5 = 4 - 5 = -1
   \]

2. **Now find \( g(f(2)) = g(-1) \):**
   \[
   g(x) = 1 - x
   \]
   Substituting \( x = -1 \):
   \[
   g(-1) = 1 - (-1) = 1 + 1 = 2
   \]

This implies:
\[
(g \circ f)(2) = g(f(2)) = g(-1) = 2
\]

However, you mentioned that \( (g \circ f)(2) = 0 \), which does not match the calculated result of 2.

It seems there may be a typo or miscommunication in the problem. Please review the function definitions or constraints provided.

Would you like to clarify the functions or constraints further?

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Here are 5 related questions to deepen your understanding:

1. How does the order of function composition affect the result?
2. What would happen if we reversed the composition to find \( (f \circ g)(2) \)?
3. Can you generalize how to solve function compositions for different types of functions?
4. What other values of \( x \) make \( g(f(x)) = 0 \)?
5. How would this process change if the functions involved were non-linear (e.g., quadratic)?

**Tip:** When composing functions, always evaluate the inner function first, then use the result in the outer function.

If f(x) = 2x - 5 and g(x) = 1 - x, then (g • f)(2) = 0.

Learn how to solve the composition of two linear functions, f(x) = 2x - 5 and g(x) = 1 - x, by finding (g • f)(2). This step-by-step guide explains key concepts in function composition and is ideal for students in Grades 9-11.

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