Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.


logb x/y

Finding all inverses Find all the inverses associated with the following functions, and state their domains.

ƒ(x) = 2 / ( x² + 2)

More composite functions Let ƒ(x) = | x | , g(x)= x² - 4 , F(x) = √x , G(x) = (1)/(x-2) Determine the following composite functions and give their domains.

G o G

Sketch the graph of the inverse of ƒ. <IMAGE>

Find the inverse of the function ƒ(x) = 2x. Verify that ƒ(ƒ⁻¹(x)) = x and ƒ⁻¹(ƒ(x)) = x .

Solving equations Solve the following equations.

ln x= -1

The National Weather Service releases approximately $70,000$ radiosondes every year to collect data from the atmosphere. Attached to a balloon, a radiosonde rises at about $1000$ ft/min until the balloon bursts in the upper atmosphere. Suppose a radiosonde is released from a point $6$ ft above the ground and that $5$ seconds later, it is $83$ ft above the ground. Let $f\(\left\)(t\(\right\))$ represent the height (in feet) that the radiosonde is above the ground $t$ seconds after it is released. Evaluate $\(\frac{f\left(5\right)-f\left(0\right)}{5-0}\)$ and interpret the meaning of this quotient.