Question

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

Answer 1

`A^(-1)(n)=(1)/(3)n+(20)/(3)`

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:

`(x+20)/(3)=y`, or to write it in slope-intercept form, like the function you started with:

`y=(1)/(3)x+(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)=(1)/(3)n+(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).