Young male children have been studied and the relationship

Question

1. Find the inverse function f^-1  of   f(x) = 9x – 6.

2. Find the inverse of the function.  Determine whether the inverse is also a function.

     x     f(x)

     –10      10

     –2      4

     4      4

     9      10

4. Determine whether the function is one-to-one.

f = {–4, –2), (–3, 4), (–1, –5), (0, 5), (3, 10)}

5. Determine whether or not the inverse of the given function is a function.

     x     g(x)

     –4 7

     10 8

     9 9

     1 10

6. If the function f(x) = x² + 4 is restricted to the domain D = {x | x >= 0}, what will be the domain of the inverse function?

8. Solve the exponential equation for x.

6^x  = 36^{x +1}

9. Suppose the doubling time for a bacterial culture is 8 days.  That is, after a 8-day period, the original number of bacteria will have doubled.  If the original number of bacteria was 580, the formula relating the number after time x is given by

N(x) = 580•2^x/8

Use a calculator to find the number of bacteria present after 32 days.  Round your answer to the nearest bacteria.

12. Convert the exponential form of the equation to logarithmic form.

7⁴  = 2401

20. Young male children have been studied and the relationship between their body length L, in centimeters, is related to their age A, in months, by the equation

L=42.37+32.77.logA

 Find the body length of a 23-month old child, correct to the nearest 0.1 cm.

21. Use a calculator to approximate the antilogarithm of 1.325, correct to two decimal places.

22. Solve the exponential equation for x.

3^5x+2 =9^5x