91Ó°ÊÓ

The total amount borrowed ( whether by an individual from a bank in the form of a loan or by a bank from an individual in the form of a savings account) is called the _____.

Determine which of the following points are on the graph of $x^2+y^2=1$.

$$\begin{gathered} \left(a\right)(\frac{1}{2},\frac{1}{2}) \\ \left(b\right)(\frac{1}{2},\frac{\sqrt{3}}{2}) \end{gathered}$$

Find the domain of the function$f\left(x\right)=\frac{x^2-1}{x^2-25}$.

Chemist has a 100-gram sample of a radioactive

material. He records the amount of radioactive material every week for 7 weeks and obtains the following data:

(a) Using a graphing utility, draw a scatter diagram with week as the independent variable.

(b) Using a graphing utility, build an exponential model from the data.

(c) Express the function found in part (b) in the form A(t) = A0 e^kt.

(d) Graph the exponential function found in part (b) or (c) on the scatter diagram.

(e) From the result found in part (b), determine the half-life of the radioactive material.

(f) How much radioactive material will be left after 50 weeks?

(g) When will there be 20 grams of radioactive material?

Find the inverse of $f\left(x\right)=\frac{2}{3x-5}$ and check your answer. State the domain and the range of $fand{f}^{-1}$.

Approximate the solution to$x^3=x^2−5$ using a graphing utility.

In Problems 2 – 4, for the given functions f and g find:

(a) (f o g)(2)

(b) (g o f) (-2)

(c) (f o f)(4)

(d) ( g o g) (-1)

$f\left(x\right)=\sqrt{x+2}:g\left(x\right)=2x^2+1$

Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write each logarithm in terms of a and b.

$\ln \frac{2}{3}$

For the given functions f and g, find:

$a)f∘gb)g∘fc)f∘fd)g∘g$

State the domain of each composite function.

$f\left(x\right)=-x and g\left(x\right)=2x-4$

Find the exact value of the logarithm without using a calculator.

${\log }_{\frac{1}{3}}\left(9\right)$.