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Chapter 2: Problem 3
Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(3,4),(3,5),(4,4),(4,5)\\} $$
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Find all values of x satisfying the given conditions. $$f(x)=2 x-5, g(x)=x^{2}-3 x+8, \text { and }(f \circ g)(x)=7$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \begin{aligned} &\text { If } f(x)=x^{2}-4 \text { and } g(x)=\sqrt{x^{2}-4}, \text { then }(f \circ g)(x)=-x^{2}\\\ &\text { and }(f \circ g)(5)=-25 \end{aligned} $$
Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\frac{1}{4 x+5}$$
Solve for \(y: \quad A x+B y=C y+D\) (Section \(1.3, \text { Example } 8)\)
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I must have made a mistake in finding the composite functions \(f \circ g\) and \(g \circ f,\) because I notice that \(f \circ g\) is not the same function as \(g \circ f\)
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