Let ƒ(x) = 1/ (x³+1).
Compute ƒ(2) and ƒ(y²).

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

ƒ(x) = (x + 1)³

Simplify the difference quotients ƒ(x+h) - ƒ(x) / h and ƒ(x) - ƒ(a) / (x-a) by rationalizing the numerator.

ƒ(x) = - (3/√x)

Suppose ƒ is an even function with ƒ(2) = 2 and g is an odd function with g(2) = -2. Evaluate ƒ(-2) , ƒ(g(2)), and g(ƒ(-2))

Simplify the difference quotient ƒ(x+h)-ƒ(x)/h

ƒ(x) = 2x² -3x +1

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

logb (√x) / (³√z)

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.