91Ó°ÊÓ

Find the domain of the function.

$f\left(x\right)=3-2{\log }_4\left(\frac{x}{2}-5\right)$

Time Required to Reach a Goal

How many years will it take for an initial investment of \(10,000 to grow to \)25,000? Assume a rate of interest of 6% compounded continuously.

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility:$8=4^{x^2}×2^{5x}$

In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

$y=2^x+1$

Write each expression as a sum and/or difference of logarithms. Express powers as factors.

$\ln \left(\frac{e}{x}\right)$

Find the domain of the function.

$g\left(x\right)=8+5\ln \left(2x+3\right)$

In Problems 29 – 44, for the given functions f and g, find$\left(a\right)f∘g\left(b\right)g∘f\left(c\right)f∘f\left(d\right)g∘g$

State the domain of each composite function.

$f\left(x\right)=x^2+4;g\left(x\right)=\sqrt{x-2}$

Verify that the functions $f\left(x\right)=\frac{x-5}{2x+3}$and $g\left(x\right)=\frac{3x+5}{1-2x}$are inverses of each other by showing that $f\left(g\left(x\right)\right)=x$ and $g\left(f\left(x\right)\right)=x$. Give any values ofx that need to be excluded from the domain of f and the domain ofg.

Time Required to Reach a Goal

How many years will it take for an initial investment of \(25,000 to grow to \)80,000? Assume a rate of interest of 7% compounded continuously.