The Domain and range of functions

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Do the domain and range have to be in accordance with each other? Meaning that for this question

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the range is $f^{-1}(x) > 4$ and so is the domain $\frac{13}{8} < x < 3$, or $x < 3$?

The range is only true for the domain values between $\frac{13}{8} < x < 3$, but the mark scheme says the domain is $x < 3$,