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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