given the function f(x)=(x + 2)^3, complete parts a through c.\n(a) find an equation for f^(-1)(x).\n(b)…

given the function f(x)=(x + 2)^3, complete parts a through c.\n(a) find an equation for f^(-1)(x).\n(b) graph f and f^(-1) in the same rectangular coordinate system.\n(c) use interval notation to give the domain and the range of f and f^(-1).\n(a) find f^(-1)(x).\nf^(-1)(x)= \n(type an exact answer, using radicals as needed.)

given the function f(x)=(x + 2)^3, complete parts a through c.\n(a) find an equation for f^(-1)(x).\n(b) graph f and f^(-1) in the same rectangular coordinate system.\n(c) use interval notation to give the domain and the range of f and f^(-1).\n(a) find f^(-1)(x).\nf^(-1)(x)= \n(type an exact answer, using radicals as needed.)

Answer

Explanation:

Step1: Set (y = f(x))

Let (y=(x + 2)^3).

Step2: Solve for (x) in terms of (y)

Take the cube - root of both sides: (\sqrt[3]{y}=x + 2). Then (x=\sqrt[3]{y}-2).

Step3: Replace (x) with (f^{-1}(x)) and (y) with (x)

(f^{-1}(x)=\sqrt[3]{x}-2).

Answer:

(f^{-1}(x)=\sqrt[3]{x}-2)