If \( g(x) \) is the inverse of \( f(x) \) and \( f(x) \) has domain \( x \in[1,5] \), where \( ...

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If \( g(x) \) is the inverse of \( f(x) \) and \( f(x) \) has domain \( x \in[1,5] \), where \( f(1)=2 \) and \( f(5)=10 \) then find the value of
\[
\int_{1}^{5} f(x) d x+\int_{2}^{10} g(y) d y
\]
(a) 24
(b) 96
(c) 12
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