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Chapter 3: Problem 9
Suppose \(m\) and \(n\) are positive integers such that \(\log m \approx 32.1\) and \(\log n \approx 7.3 .\) How many digits does \(m n\) have?
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Show that the range of cosh is the interval \([1, \infty)\).
Estimate the indicated value without using a calculator. \(\frac{e^{5}}{e^{4.984}}\)
Find \(a\) formula for \((f \circ g)(x)\) assuming that \(f\) and \(g\) are the indicated functions. \(f(x)=\ln x\) and \(g(x)=e^{4-7 x}\)
Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=6^{x}+7 $$
For each of the functions \(f\); (a) Find the domain of \(f\). (b) Find the range of \(f\). (c) Find a formula for \(f^{-1}\). (d) Find the domain of \(f^{-1}\). (e) Find the range of \(f^{-1}\). You can check your solutions to part ( \(c\) ) by verifying that \(f^{-1} \circ f=I\) and \(f \circ f^{-1}=I .\) (Recall that \(I\) is the function defined by \(I(x)=x .)\) \(f(x)=4-2 e^{8 x}\)
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