find the inverse?

Question

V=f(r)=4(pi)r^3 is the original function

what is f^-1 (f inverse) V?

Answer 1

f^-1(r)=(r/(4pi))^(1/3)



n^(1/3) is the same as the cube root

Answer 2

Assume the original function is:

y = 4(pi)(x^3)

Now, switch the x and y in the above equation and solve for y.

x = 4(pi)(y^3)
y^3 = x/(4pi)
y = cube root (x/(4pi))

Answer 3

f(r) = 4pi(r^3)

To find the inverse, let y = f(r). Then

y = 4pi(r^3)

Now, we swap the y and r variables.

r = 4pi(y^3)

And now we solve for y.

r/(4pi) = y^3, so

y = [r/(4pi)]^(1/3)

Therefore,

f^(-1)(r) = [r/(4pi)]^(1/3)