Find inverse of f(x)=(x-3)^3+2

Answer 1

See the videa.

Answer 2

1. y = (x-3)^3 + 2
2. switch x & y: x = (y-3)^3 + 2
3. Solve for y:

x - 2 = (y-3)^3

(x - 2)^ (1/3) = y - 3

(x - 2)^ (1/3) + 3 = y

1. Rewrite it with f^(-1)(x) = (x - 2) ^ (1/3) + 3

Answer 3

f(x) = (x-3)^3 +2 = y

switch x and y and solve for the new y

x = (y-3)^3 +2

(y-3)^3 = x-2

y-3 = (x-2)^(1/3

y = (x-2)^(1/3) + 3 = f^-1(x)