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Chapter 2: Problem 7
Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(-3,-3),(-2,-2),(-1,-1),(0,0)\\} $$
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding h and k, I place parentheses around the numbers that follow the subtraction signs in a circle鈥檚 equation.
Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$f(x)=x^{2}+1, g(x)=x^{2}-3$$
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+6 x+2 y+6=0$$
Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=(2 x-5)^{3}$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \begin{aligned} &\text { If } f(x)=x^{2}-4 \text { and } g(x)=\sqrt{x^{2}-4}, \text { then }(f \circ g)(x)=-x^{2}\\\ &\text { and }(f \circ g)(5)=-25 \end{aligned} $$
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