What are the domain and range of the function f of x is equal to negative log times open paren 5 minus x close paren plus 9 ?

For f(x) = −log(5 − x) + 9, the logarithm’s input must be positive: 5 − x > 0, so x < 5. A logarithm can take any positive input and its values span all real numbers; reflecting it with a negative sign and shifting it up by 9 still leaves the range as all real numbers. Therefore, choice B is correct: domain x < 5 and range (−∞, ∞).

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