Find the difference quotient of \(f\); that is find \(\frac{f(x+h)-f(x)}{h}\), \(h \neq 0\), for the function \(f(x) = \sqrt{x-9}\). [Hint: Rationalize the numerator.] The difference quotient of \(f\); \(f(x) = \sqrt{x-9}\) is \(\boxed{}\). (Simplify your answer.)
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To do this, we multiply the numerator and denominator by the conjugate of the numerator, which is (f(x+h) + √x - 9): (f(x+h) - √x + 9)(f(x+h) + √x - 9)/(h(f(x+h) + √x - 9)) Expanding the numerator, we get: f(x+h)^2 - (√x + 9)(f(x+h)) + 81 - x Substituting Show more…
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