The following function is one-to-one. Find its inverse and verify your answer:

Question

F(x) = ³squareroot (x-1) + 4

Answer 1

y = cube root of (x-1) + 4

y = (x-1)^1/3 +4

switch x and y, then solve for y to find the inverse function

x = (y-1)^1/3 +4

x-4 = (y-1)^1/3 cube both sides

(x-4)^3 = y-1

y = (x-4)^3 + 1 is the inverse function, f^-1(x)

or if you want use the cube formula (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 where a=x and b =-4

y = x^3 -12x^2 +48x - 64 + 1

y = x^3 -12x^2 +48x -63 = f^-1(x)