Question

What is the equation of the inverse function A(n)=3n-20

Answer 1

Answer:

$A^{-1}(n)=\frac{1}{3}n+\frac{20}{3}$

Step-by-step explanation:

First, let's change those variables to x and y, just for the sake of convenience.  In order to find the inverse of a function algebraically, switch the x and y coordinates, then solve for the new y.  Letting y = A(n) and x = n (we will switch them back when we're done):

y = 3x - 20.  This is linear; a line with a slope of 3 and a y-intercept of -20.  When we switch the x and the y, we get:

x = 3y - 20.  Now we solve for the new y.  Begin by adding 20 to both sides:

x + 20 = 3y.  Now divide both sides by 3:

$\frac{x+20}{3}=y$, or to write it in slope-intercept form, like the function you started with:

$y=\frac{1}{3}x+\frac{20}{3}$

This is also a line, with a slope of 1/3 and a y-intercept of +20/3

Now, replacing:

$A^{-1}(n)=\frac{1}{3}n+\frac{20}{3}$

That is how to write the inverse using function notation.  The little -1 as an exponent tells us that this is the inverse of the function A(n).