Determine whether each of the following graphs represents a one-to-one
function.
2. For each part below, determine if an inverse for the given f( x )
exists. If an inverse exists, then please find the inverse.
Otherwise, write “NO INVERSE”.
3. In order to check to make sure we have the right inverse for a
given f( x ), we can check that and also that
. Using that idea of checking, please check to
make sure that the inverse you got in #2 (a) is the correct inverse
for f( x ) = 3x + 3.
4. The following formula can be used to convert Fahrenheit temperatures
x to Celsius temperatures T(x):
Find T(-13) and T(86).
Find T-1(x) and explain what it represents.
5. Please choose which equation represents the following graph:
f( x ) = -ex
f( x ) = -ex + 1
f( x ) = e-x + 1
6. Please choose which equation represents the following graph:
f( x ) = 2x - 1
f( x ) = 2x - 1
f( x ) = -2x - 1
f( x ) = -2x – 1
7. Water initially at 130 degrees Fahrenheit is left in a room of temperature
70 degrees Fahrenheit to cool. After t minutes, the temperature T of the
water is given by
Find the temperature of the water 10 minutes after it is left to cool.
8. Suppose that $100,000 is invested at 4% interest, compounded
monthly. Find the amount of money in the account after 10 years.
9. Find each of the following, and round answer to the nearest 4 decimal places.
10. Find log4 50 using the change of base formula, and round answer to the
nearest 4 decimal places.
11. Students in an accounting class took a final exam and then took equivalent
forms of the exam at monthly intervals thereafter. The average score
S(t), as a percent, after t months was found to be given by the function
S(t) = 78 – 15 log(t + 1)
What was the average score when the students initially took the
test?
What was the average score after 4 months? after 24 months?
12. Express log 2x as a sum of logarithms.
13. Express as a product.
14. Express as a difference of logarithms.
FOR #15 AND #16, EXPRESS IN TERMS OF SUMS AND DIFFERENCES
OF LOGARITHMS.
15
16.
FOR #17 AND #18, EXPRESS AS A SINGLE LOGARITHM, AND IF POSSIBLE, SIMPLIFY.
17. ln 44 – ln 4
18.
FOR #19 AND #20, LET , , AND , FIND EACH OF THE FOLLOWING:
