Problem 93 of 7
Find the domain restriction for the combined function (f/g)(x) where g(x)=(x-1)(x+4) given f: x >= 0, g: all real numbers.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
identify common input restrictions and quotient exclusions.
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Domain must be intersection of component domains, with quotient denominator exclusions.
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Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Start with inputs allowed by both component functions.
2. For quotients, remove inputs that make the denominator zero.
3. State the remaining common domain.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Using union of domains for combined functions.