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Magazine Problem 43
Find \(f^{-1}\). Check that \(\left(f \circ f^{-1}\right)(x)=x\) and \(\left(f^{-1} \circ f\right)(x)=x\) Strategy for Finding \(f^{-1}\) by Switch-and Solve. $$f(x)=\sqrt[3]{3 x+7}$$
Problem 43
Let \(f(x)=2 x-3, g(x)=x^{2}+3 x,\) and \(h(x)=\frac{x+3}{2} .\) Find the following. See Examples 4 and \(5 .\) $$(f \circ g)(x)$$
Problem 44
Let \(f(x)=2 x-3, g(x)=x^{2}+3 x,\) and \(h(x)=\frac{x+3}{2} .\) Find the following. See Examples 4 and \(5 .\) $$(h \circ g)(x)$$
Problem 44
Find \(f^{-1}\). Check that \(\left(f \circ f^{-1}\right)(x)=x\) and \(\left(f^{-1} \circ f\right)(x)=x\) Strategy for Finding \(f^{-1}\) by Switch-and Solve. $$f(x)=\sqrt[3]{7-5 x}$$
Problem 45
Find \(f^{-1}\). Check that \(\left(f \circ f^{-1}\right)(x)=x\) and \(\left(f^{-1} \circ f\right)(x)=x\) Strategy for Finding \(f^{-1}\) by Switch-and Solve. $$f(x)=\frac{x+1}{x-2}$$
Problem 45
Find the requested values. See Example 4. If \(D\) varies directly with \(t\) and inversely with the square of \(s,\) and \(D=12.35\) when \(t=2.8\) and \(s=2.48,\) find \(D\) when \(t=5.63\) and \(s=6.81\).
Problem 46
Find \(f^{-1}\). Check that \(\left(f \circ f^{-1}\right)(x)=x\) and \(\left(f^{-1} \circ f\right)(x)=x\) Strategy for Finding \(f^{-1}\) by Switch-and Solve. $$f(x)=\frac{1-x}{x+3}$$
Problem 47
Let \(f(x)=2 x-3, g(x)=x^{2}+3 x,\) and \(h(x)=\frac{x+3}{2} .\) Find the following. See Examples 4 and \(5 .\) $$(f \circ f)(x)$$
Problem 47
Find \(f^{-1}\). Check that \(\left(f \circ f^{-1}\right)(x)=x\) and \(\left(f^{-1} \circ f\right)(x)=x\) Strategy for Finding \(f^{-1}\) by Switch-and Solve. $$f(x)=\frac{x+1}{3 x-4}$$
Problem 48
Let \(f(x)=2 x-3, g(x)=x^{2}+3 x,\) and \(h(x)=\frac{x+3}{2} .\) Find the following. See Examples 4 and \(5 .\) $$(g \circ g)(x)$$
