Question

Use inverse operations to find the inverse of y = 27x?
The inverse of y = 27x3 is y =

Answer 1

y = (∛x)/3

Explanation:

To undo the multiplication by 27, you multiply by its inverse:

(1/27)y = (1/27)(27x^3)

y/27 = x^3 . . . . . . . . . . . simplify

To undo the cube, you take the cube root:

(∛y)/(∛27) = ∛(x^3)

(∛y)/3 = x

Apparently, you want the inverse function, so you swap the variables:

y = (∛x)/3

_____

You can swap the variables at the beginning or end. It doesn't matter. If you do it at the beginning, you have ...

x = 27y^3

and you're solving for y. You use the same inverse operations that we used above.