Find f/g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

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First, write down the given functions: \(f(x) = 2x + 3\) and \(g(x) = x - 1\).

To find \(\frac{f}{g}\), form the quotient of the two functions: \(\frac{f}{g} = \frac{2x + 3}{x - 1}\).

Next, determine the domain of \(\frac{f}{g}\). The domain includes all real numbers except where the denominator is zero, because division by zero is undefined.

Set the denominator equal to zero and solve for \(x\): \(x - 1 = 0\) which gives \(x = 1\). This value must be excluded from the domain.

Therefore, the domain of \(\frac{f}{g}\) is all real numbers \(x\) such that \(x \neq 1\).

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