Asked by chris
If m(x)= x+5/x-1 and n(x) = x – 3, which function has the same domain as (m times n)(x)?
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GPT-5 mini
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Interpreting m(x) = (x+5)/(x-1) and n(x) = x-3, their product is
(m·n)(x) = (x+5)(x-3)/(x-1) = (x^2 + 2x - 15)/(x-1).
The domain is all real numbers except x = 1 (where m is undefined). Any function with the same excluded value has the same domain; for example, (x^2 + 2x - 15)/(x - 1) (or simply 1/(x-1)) has the same domain: all real x ≠ 1.
(m·n)(x) = (x+5)(x-3)/(x-1) = (x^2 + 2x - 15)/(x-1).
The domain is all real numbers except x = 1 (where m is undefined). Any function with the same excluded value has the same domain; for example, (x^2 + 2x - 15)/(x - 1) (or simply 1/(x-1)) has the same domain: all real x ≠ 1.
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