# Algebra and Functions with Domain and Range

1) Given the function f(x)=sqrt(x+8), find the DOMAIN of the inverse function, f^-1(x).

a) [0,Ã¢??)

b) (-Ã¢??, 0]

2) Suppose that a person x inches tall sprains an ankle. An approximation for the length of a crutch (in inches) that a person might need is given by the function f(x)=19/26x+2. Find and interpret f^-1(49.5).

a) f^-1(49.5)=38.2; A crutch length of 49.5 inches would be appropriate for a person 38.2 inches tall.

b) f^-1(49.5)=65; A crutch length of 65 inches would be appropriate for a person 49.5 inches tall.

c) f^-1(49.5)=38.2; A crutch length of 38.2 inches would be appropriate for a person 49.5 inches tall.

d) f^-1(49.5)=65; A crutch length of 49.5 inches would be appropriate for a person 65 inches tall.

3)Given that f(x) is an exponential function of the form f(x)=k*b^x, use the table below to determine the values of k and b.

x -2 -1 1 4 5

f(x) 27 / 100 9 / 20 5 / 4 625 / 108 3125 / 324

k=_____

b=_______

4) Determine the values of k and b with the points shown below y=k*b^x.

(-1,12) (0,4)

k=______

b=_______

(-1,6) (0,2)

k=_______

b=_______

5) The temperature, in degrees Fahrenheit, of a cup of coffee can be expressed by T(t)=70+110e^-0.04t, where t is measured in minutes. Use this equation to answer the following questions. Round to the nearest degree.

What is the initial temperature of the coffee?

________degrees

https://brainmass.com/math/basic-algebra/algebra-functions-domain-range-321175

## SOLUTION This solution is **FREE** courtesy of BrainMass!

(1) a

(2) d

(3) k = 0.75 and b = 1.6652

(4) (i) k = 4 and b = 0.3362 (ii) k = 2 and b = 0.3362

(5) 180.

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