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.