Using the domain concept, it is found that \(f(x) = \frac{1}{x - 3}\) has the same domain as \((m \times n)(x) = \frac{x^2 + 4x - 5}{x - 3}\)
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- The domain of a function is given by all possible values of the input.
- The functions are:
\(m(x) = \frac{x + 5}{x - 1}\)
\(n(x) = x - 3\)
- Their multiplication is given by:
\((m \times n)(x) = \frac{x + 5}{x - 1} \times x - 3 = \frac{(x + 5)(x - 1)}{x - 3} = \frac{x^2 + 4x - 5}{x - 3}\)
- In a fraction, the denominator cannot be 0, thus, the domain is all real numbers except 3. A function with the same domain is one in which the numerator is changed while the denominator is the same, for example, \(f(x) = \frac{1}{x - 3}\)
A similar problem is given at https://brainly.com/question/10891721
