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DOMAIN AND RANGE HELP PLEASE!!! ASAP!!!!!











































Find f^-1(x) of f(x)=2^-x+3. State the domain and range of f(x)=2^-x+3

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Apr 22, 2011
Inverse Function, Domain, and Range
by: Staff


The question:

Find f^-1(x) of f(x)=2^-x+3. State the domain and range of f(x)=2^-x+3

The answer:

Inverse Function

f^-1(x) stands for the inverse function of f(x).

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To understand what an inverse function is, consider how we use the phone book.

To look up a phone number you look up a name. The names are arranged alphabetically. Once you find the name, the phone number is easy to find because it is printed alongside the name.

The inverse function for the phone book is the exact opposite. The names in the phone book will not be listed alphabetically. Instead, the phone numbers will be listed in numerical order. You begin by looking up a phone number. The name will be listed alongside.

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Find f^-1(x) of f(x)=2^-x+3.

Original function:

f(x)=2^-x+3

solve for x

f(x) = 2^-x + 3

subtract 3 from each side of the equation

f(x) - 3 = 2^-x + 3 - 3

f(x) - 3 = 2^-x + 3 - 3

f(x) - 3 = 2^-x + 0

f(x) - 3 = 2^-x

2^-x = f(x) - 3

Take the log of each side of the equation

log(2^-x) = log(f(x) - 3)

-x * log(2) = log(f(x) - 3)

-x * log(2) / log(2) = log(f(x) - 3) / log(2)

-x * 1 = log(f(x) - 3) / log(2)

-x = log(f(x) - 3) / log(2)

Multiply each side of the equation by -1

(-1) * (-x) = (-1) * log(f(x) - 3) / log(2)

x = (-1) * log(f(x) - 3) / log(2)

x = -log(f(x) - 3) / log(2)

Replace the x on the left side of the equation with f^-1(x). Replace the f(x) on the right side of the equation with x.

f^-1(x) = -log(x - 3) / log(2)

the inverse function is:

f^-1(x) = -log(x - 3) / log(2)



Click the following link to view a graph of the original function f(x) and its inverse f^-1(x); use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/inverse-graph.png



Domain and Range

f(x)=2^-x+3

domain: all x

range: f(x) > 3


Click the following link to view graph; use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/function-asymptote-graph.png



Thanks for writing.


Staff
www.solving-math-problems.com


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