How do you find the inverse of #f(x) = 4/x# and is it a function?

1 Answer
David B.
Mar 31, 2016

The inverse is #x=4/y# which is a function.

Explanation:

First, let's assign a variable to the value of the function

#f(x)=y=4/x#

Now we solve for #x# in terms of #y#. Multiply both sides by #x# and divide both sides by #y# to get the inverse

#x=4/y#

For an equation to be a function, there must be a single value of #x# for each #y# in the range, which is the case. Interestingly, the inverse is the same as the original function! This particular function is called a rectangular hyperbola.

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