Math  /  Algebra

QuestionFirst find f+g,fg,fgf+g, f-g, f g, and fg\frac{f}{g}. Then determine the domain for each function. f(x)=x+8;g(x)=x1f(x)=\sqrt{x+8} ; g(x)=\sqrt{x-1}

Studdy Solution
Determine the domain of fg \frac{f}{g} .
The domain of fg \frac{f}{g} is the same as the domain of f+g f+g since g(x)0 g(x) \neq 0 in this domain: Domain of (fg)=[1,) \text{Domain of } \left(\frac{f}{g}\right) = [1, \infty)
Solution: \begin{align*} (f+g)(x) &= \sqrt{x+8} + \sqrt{x-1} \quad \text{with domain } [1, \infty) \\ (f-g)(x) &= \sqrt{x+8} - \sqrt{x-1} \quad \text{with domain } [1, \infty) \\ (fg)(x) &= \sqrt{(x+8)(x-1)} \quad \text{with domain } [1, \infty) \\ \left(\frac{f}{g}\right)(x) &= \sqrt{\frac{x+8}{x-1}} \quad \text{with domain } [1, \infty) \end{align*}

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