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Magazine Problem 82
For the following exercises, use \(f(x)=x^{3}+1\) and \(g(x)=\sqrt[3]{x-1}\). What is the domain of $$ (g \circ f)(x) ? $$
Problem 82
For the following exercises, graph \(y=\sqrt{x}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. \([0,0.01]\)
Problem 83
For the following exercises, graph \(y=\sqrt{x}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. \([0,100]\)
Problem 83
For the following exercises, use \(f(x)=x^{3}+1\) and \(g(x)=\sqrt[3]{x-1}\). What is the domain of \((f \circ g)(x) ?\)
Problem 84
Let \(f(x)=\frac{1}{x}\). (a) Find \((f \circ f)(x)\). (b) Is \((f \circ f)(x)\) for any function \(f\) the same result as the answer to part (a) for any function? Explain.
Problem 85
For the following exercises, let \(F(x)=(x+1)^{5}, f(x)=x^{5},\) and \(g(x)=x+1\). True or False: \((g \circ f)(x)=F(x)\).
Problem 85
For the following exercises, graph \(y=\sqrt[3]{x}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [-0.001,0.001]
Problem 86
For the following exercises, let \(F(x)=(x+1)^{5}, f(x)=x^{5},\) and \(g(x)=x+1\). True or False: \((f \circ g)(x)=F(x)\).
Problem 86
For the following exercises, graph \(y=\sqrt[3]{x}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [-1000,1000]
Problem 87
For the following exercises, graph \(y=\sqrt[3]{x}\) on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [-1,000,000,1,000,000]
