As with finding inverses of quadratic functions, it is sometimes desirable to find the
inverse of a rational function , particularly of rational functions that are the ratio of linear functions, such as in concentration applications.
Finding the inverse of a rational function
The function
represents the concentration
of an acid solution after
mL of 40% solution has been added to 100 mL of a 20% solution. First, find the inverse of the function; that is, find an expression for
in terms of
Then use your result to determine how much of the 40% solution should be added so that the final mixture is a 35% solution.
We first want the inverse of the function in order to determine how many mL we need for a given concentration. We will solve for
in terms of
Now evaluate this function at 35%, which is
We can conclude that 300 mL of the 40% solution should be added.
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