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Chapter 1: Problem 38
Determine the domain of the function represented by the given equation. $$f(x)=\frac{1}{\sqrt{5-x}}$$
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solve by completing the square or by using the quadratic formula. $$3 x^{2}-5 x-4=0$$
The notation \(\left.f(x)\right|_{a} ^{b}\) is used to denote the difference \(f(b)-f(a) .\) That is, $$\left.f(x)\right|_{a} ^{b}=f(b)-f(a)$$ Evaluate \(\left.f(x)\right|_{0} ^{b}\) for the given function \(f\) and the indicated values of \(a\) and \(b\). $$f(x)=\sqrt{8-x} ;\left.f(x)\right|_{0} ^{8}$$
Each function has two or more independent yariables. Given \(f(x, y)=3 x+5 y-2,\) find a. \(f(1,7)\) b. \(f(0,3)\) c. \(f(-2,4)\) d. \(f(4,4)\) e. \(f(k, 2 k)\) f. \(f(k+2, k-3)\)
The area of a triangle with sides \(a\) \(b,\) and \(c\) is given by the function $$A(a, b, c)=\sqrt{s(s-a)(s-b)(s-c)}$$ where \(s\) is the semiperimeter $$s=\frac{a+b+c}{2}$$ Find \(A(5,8,11)\)
The notation \(\left.f(x)\right|_{a} ^{b}\) is used to denote the difference \(f(b)-f(a) .\) That is, $$\left.f(x)\right|_{a} ^{b}=f(b)-f(a)$$ Evaluate \(\left.f(x)\right|_{0} ^{b}\) for the given function \(f\) and the indicated values of \(a\) and \(b\). $$f(x)=x^{2}-\left.x f(x)\right|_{2} ^{3}$$
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