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}

the last answer

Step-by-step explanation:

S(x) = 4pix^2

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

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

solve for y

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

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1