91Ó°ÊÓ

Find the \(x\) -intercept(s) and \(y\) -intercept(s) of the graph of \(f(x)=2 x^{2}-5 x+1\)

Suppose that \(\ln 2=a\) and \(\ln 3=b .\) Use properties of logarithms to write each logarithm in terms of a and \(b\). \(\ln \sqrt[4]{\frac{2}{3}}\)

For the given functions fand \(g\), find: (a) \(f^{\circ} g\) (b) \(g^{\circ} f\) (c) \(f \circ f\) (d) \(g^{\circ}\) g State the domain of each composite function. \(f(x)=x^{2}+4 ; \quad g(x)=\sqrt{x-2}\)

For the given functions fand \(g\), find: (a) \(f^{\circ} g\) (b) \(g^{\circ} f\) (c) \(f \circ f\) (d) \(g^{\circ}\) g State the domain of each composite function. \(f(x)=\frac{x-5}{x+1} ; \quad g(x)=\frac{x+2}{x-3}\)

Solve: \(\frac{x+1}{x}-\frac{x}{x+1}=2\)

Verify that the functions \(f\) and g are inverses of each other by showing that \(f(g(x))=x\) and \(g(f(x))=x\). Give any values of x that need to be excluded from the domain of \(f\) and the domain of g. $$ f(x)=x^{3}-8 ; \quad g(x)=\sqrt[3]{x+8} $$

What rate of interest compounded quarterly will yield an effective interest rate of \(7 \%\) ?

In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. \(\log _{6} 36 x\)

Solve each logarithmic equation. Express irrational solutions in exact form. $$ 2 \log _{5}(x-3)-\log _{5} 8=\log _{5} 2 $$

Find the exact value of each logarithm without using a calculator. $$ \ln \sqrt{e} $$