Question

The surface area of a sphere is S(x) = 4πx2, where x is the length of the radius of the sphere. Restrict the domain to create a one-to-one function. Find and describe the inverse function

Answer 1

The answer is
`s^(-1 )(x) = (1)/(2\sqrt(\pi ))\sqrt(x)` .

Explanation:

The input of
`s^(-1 )` is the surface area of a sphere; the output is the length of the radius.

Answer 2

Given that the surface area of the sphere is S(x)=4πx², the inverse function will be obtain as follows: make x the subject of the function
S(x)/(4π)=x²
get the square root of both sides:
x=√[S(x)/(4π)]
replace x by S⁻¹(x) and S(x) by x
this will give us the inverse as :
S⁻¹(x)=√[x/(4π)]
The above implies that the inverse is the square root of the radius divided by 4π