Answer:
[tex]A^{-1}(n)=\frac{1}{3}n+\frac{20}{3}[/tex]
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:
[tex]\frac{x+20}{3}=y[/tex], or to write it in slope-intercept form, like the function you started with:
[tex]y=\frac{1}{3}x+\frac{20}{3}[/tex]
This is also a line, with a slope of 1/3 and a y-intercept of +20/3
Now, replacing:
[tex]A^{-1}(n)=\frac{1}{3}n+\frac{20}{3}[/tex]
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).
