Problem

\[
f=\{(-1,1),(1,-2),(3,-4)\}
\]
and
\[
g=\{(5,0),(-3,4),(1,1),(-4,1)\}
\]
\[
(f-g)(1)=
\]

Answer

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Answer

Final Answer: \(\boxed{-3}\)

Steps

Step 1 :Given functions f and g as follows:

Step 2 :\[f=\{(-1,1),(1,-2),(3,-4)\}\]

Step 3 :\[g=\{(5,0),(-3,4),(1,1),(-4,1)\}\]

Step 4 :The operation \((f-g)(x)\) is defined as \(f(x) - g(x)\). So, to find \((f-g)(1)\), we need to find the values of \(f(1)\) and \(g(1)\) and then subtract \(g(1)\) from \(f(1)\).

Step 5 :From the given, \(f(1) = -2\) and \(g(1) = 1\).

Step 6 :Subtracting \(g(1)\) from \(f(1)\), we get \(-2 - 1 = -3\).

Step 7 :So, \((f-g)(1) = -3\).

Step 8 :Final Answer: \(\boxed{-3}\)

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