Find the inverse for:

Question

V=4/3•pi•r^2

Answer 1

y = f(x)

f^-1(y) =  f^-1f(x)

f^-1(y) = x

Given function f(x) =(4/3)pir^2

y =(4/3)pir^2

Multiply by 3 and divide by 4 both sides

3y/4 =(3/4)(4/3)pir^2

3y/4 =pir^2

divide by pi both sides

3y/4pi =pir^2/pi

3y/4pi =r^2

Square root on both sides

√(3y/4pi) = r

Replace

y =√(3r/4pi)

Inverse of the function is √(3r/4pi)