Calculus/Functions

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Expert: - 9/30/2009


Question
p(1+5x) = 6/(2-3x). What is p(x)?

Answer
To get the inverse, lets go with it is of the form 6/(A-Bx).

We then get p(1+5x) = 6/(A - B - 5Bx).

This says that since we have -3x and -5Bx, which are the same, B = 3/5.

Since 2 is the same as A - B and B is 3/5, 2 = A - 3/5, so A = 13/5.

Using both of these we can write p(x) = 6/(13/5 - 3x/5) = (6/1)/((13-3x)/5).

By inverting and multipying, we get p(x) = 30/(13 - 3x).

Now to test this on p(1+5x), we get 30/(13 - 3 - 15x) = 30/(10 - 15x).

Multiplying by (1/5)/(1/5) gives us p(x) = 6/(2-3x), and that is what we're after.

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