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Magazine Problem 78
Express the given function h as a composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\) $$h(x)=\sqrt{5 x^{2}+3}$$
Problem 78
Give an example of a circle's equation in standard form. Describe how to find the center and radius for this circle.
Problem 78
Begin by graphing the square root function, \(f(x)=\sqrt{x},\) Then use transformations of this graph to graph the given function. $$h(x)=\sqrt{x+1}-1$$
Problem 78
Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=x^{2}-5 x+8$$
Problem 78
Use a graphing utility to graph the function.Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=\frac{x^{3}}{2}$$
Problem 79
Use a graphing utility to graph the function.Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=\frac{x^{4}}{4}$$
Problem 79
Begin by graphing the square root function, \(f(x)=\sqrt{x},\) Then use transformations of this graph to graph the given function. $$g(x)=2 \sqrt{x+2}-2$$
Problem 79
Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=2 x^{2}+x-1$$
Problem 79
Express the given function h as a composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\) $$h(x)=|2 x-5|$$
Problem 79
How is the standard form of a circle's equation obtained from its general form?
