91Ó°ÊÓ

Determine whether the function \(f\) is one-to-one. $$f(x)=\frac{1}{x}$$

Use the theorem on inverse functions to prove that \(f\) and \(g\) are inverse functions of each other, and sketch the graphs of \(f\) and \(g\) on the same coordinate plane. $$f(x)=-x^{2}+3, x \geq 0 ; \quad g(x)=\sqrt{3-x}, x \leq 3$$

Find an exponential function of the form \(f(x)=b a^{-x}+c\) that has the given horizontal asymptote and \(y\) -intercept and passes through point \(P\). $$y=32 ; \quad y \text { -intercept } 212 ; \quad P(2,112)$$

Approximate \(x\) to three significant figures. (a) \(\log x=3.6274\) (b) \(\log x=0.9469\) (c) \(\log x=-1.6253\) (d) \(\ln x=2.3\) (e) \(\ln x=0.05\) (f) \(\ln x=-1.6\)

Children's weight The Ehrenberg relation $$\ln W=\ln 2.4+(1.84) h$$ is an empirically based formula relating the height \(h\) (in meters) to the average weight \(W\) (in kilograms) for children 5 through 13 years old. (a) Express \(W\) as a function of \(h\) that does not contain In. (b) Estimate the average weight of an 8 -year-old child who is 1.5 meters tall.