To determine the missing value in the table for the function \( g(x) = f(x) - 1 \), we need to find the value of \( f(x) \) corresponding to the given \( x \)-values.
Let's fill in the missing information from the table for \( f(x) \):
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For \( x = 0 \):
- \( f(0) = 0 \)
- Therefore, \( g(0) = f(0) - 1 = 0 - 1 = -1 \) (this is already provided).
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For \( x = -1 \):
- We have \( g(-1) \) and need to find \( f(-1) \).
- According to the table for \( g(x) \), it is provided that \( g(-1) = 2 \).
- Thus, from the relationship \( g(x) = f(x) - 1 \), we have: \[ 2 = f(-1) - 1 \]
- Therefore, solving for \( f(-1) \): \[ f(-1) = 2 + 1 = 3 \]
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For \( x = 1 \):
- According to the table for \( f(x) \), it is provided that \( f(1) = 1 \).
- Thus, we can calculate \( g(1) \): \[ g(1) = f(1) - 1 = 1 - 1 = 0 \]
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For \( x = 2 \):
- It is provided that \( f(2) = 4 \).
- Thus, we can calculate \( g(2) \): \[ g(2) = f(2) - 1 = 4 - 1 = 3 \]
After analyzing all the provided information, the missing value for \( g(-1) \) is \( 2 \) since we have that \( g(-1) \) was not given, but it corresponds to \( f(-1) \) being calculated as \( 3 \).
Therefore, the complete entries now are:
- From \( f(x) \):
- \( f(-1) = 3 \)
And from \( g(x) \):
- \( g(-1) = 2 \)
Thus, the missing value in the table for the function \( g(x) \) is \( 2 \).