Question

NEED HELP ASAP!!

the surface area of a sphere is S(x)=4pix^2, 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. {ANSWERS ARE PICTURED}

Answer 1

the last answer

Explanation:

S(x) = 4pix^2

replace S(x) with y => y = 4pix^2

switch x and y variables => x=4piy^2

solve for y

• divide both sides by 4pi => x/(4pi) = y^2
• take the square root of both sides => 1/(2(pi))(sqrtpi) = y

That eliminates the first 2 answers because S^-1(x) is incorrect, which leaves the last two answers.

• The 3rd answer is wrong because the answer says that the input of the inverse function is length of the radius, but that was the inverse of the original function, not the inverse function. For inverse functions, the input of the original function (in this case, length of radius) becomes the output and the output of the original function (in this case, surface area of the sphere) becomes the input of the inverse function.