Question

The surface area of a cube is S(x) = 6x2, where x is the length of the side of each edge of a cube. Restrict the domain to create a one-to-one function. Find and describe the inverse function.

Answer 1

Restrict values of x to
`x \ge 0`. Then the surface area function is one-to-one and has an inverse.

Write y instead of S(x). Interchange x and y, then solve for y.


`y=6x^2 \\ x=6y^2 \\ y^2=(x)/(6) \\ y=\sqrt{(x)/(6)}`

This function could be used to find the edge of a cube with a given surface area. For example, if the area is x = 54, then the edge is
`y=\sqrt{(54)/(6)} = √(9) =3`