Answer :
Restrict values of x to [tex]x \ge 0[/tex]. 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.
[tex]y=6x^2 \\ x=6y^2 \\ y^2=\frac{x}{6} \\ y=\sqrt{\frac{x}{6}} [/tex]
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 [tex]y=\sqrt{\frac{54}{6}} = \sqrt{9} =3 [/tex]
Write y instead of S(x). Interchange x and y, then solve for y.
[tex]y=6x^2 \\ x=6y^2 \\ y^2=\frac{x}{6} \\ y=\sqrt{\frac{x}{6}} [/tex]
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 [tex]y=\sqrt{\frac{54}{6}} = \sqrt{9} =3 [/tex]