Domain vs Codomain

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Consider the function \(f(x)=x+5\) on domain \[X=\{x \mid 5 \leq x \leq 29\}.\] The codomain of \(f(x)\) is \(Y=\{y \mid a \leq y \leq b\}\). If the constants \(a\) and \(b\) are such that the inverse function of \(f(x)\) exists, then what is the value of \(a+b\)?

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