Math 101- Unit 4 Review
√
1. Given f (x) = 3 x − 5 and g(x) = x2 + 7 find:
(a) (f ◦ g)(x)
(b) (f ◦ g)(2)
(c) f −1
2. Given that H(x) =
4
, find non-trivial functions f (x) and g(x) so that
(x + 2)2
(f ◦ g)(x) = H(x).
3. Given f (x) = x2 − 3, x ≥ 0. Find the domain and the range of f −1 (x).
4. Solve. Give both an exact answer an a decimal approximation to 3 decimal
places.
(a) ln(2x − 3) = 4
(b) 5x = 3x+2
(c) e2x − 2ex − 3 = 0
5. Solve.
22x−5 = 64x
6. Graph the following function by using transformations. Label the key points.
Find the domain, range and the equation of any asymptotes.
g(x) = ex−1 + 2
7. Write the following logarithm as a sum or difference of logs in expanded form.
log3
uv 2
w
8. Write as a single logarithm.
1
2 log 2 + 3 log x − log(x + 3)
2
9. The population of a city follows the exponential growth model. If the population
doubled in size over and 18-month period and the current population is 10,000,
what will the population be 2 years from now?
10. A child’s grandparents purchase a $10,000 bond fund that matures in 18 years to
be used for her college education. The bond fund pays 4% interest compounded
semiannually. How much will the bond fund be worth at maturity? How long
would it take the bond to double in value?
11. The half-life of radioactive cobalt is 5.27 years. If 100 grams of radioactive
cobalt is present now, how much will be present in 20 years? In 40 years?
12. A skillet is removed from an oven whose temperature is 450◦ F and placed in a
room whose temperature is 70◦ F. After 5 minutes, the temperature of the skillet
is 400◦ F. How long will it be until its temperature is 150◦ F