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.
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |.
The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.