## Calculus: Early Transcendentals 8th Edition

(a) The inverse function is $~~g^{-1}(x) = \sqrt[3] {1-x^3}$ $g^{-1}(x) = g(x)$ (b) If we reflect the graph of $g(x)$ in the line $y=x$, we will get exactly the same graph. The function $g(x)$ is its own inverse.
(a) We can solve $g$ for $x$: $y = \sqrt[3] {1-x^3}$ $y^3 = 1-x^3$ $y^3-1 = -x^3$ $x^3 = 1-y^3$ $x = \sqrt[3] {1-y^3}$ We reverse the places of $x$ and $y$: $y = \sqrt[3] {1-x^3}$ The inverse function is $~~g^{-1}(x) = \sqrt[3] {1-x^3}$ $g^{-1}(x) = g(x)$ (b) If we reflect the graph of $g(x)$ in the line $y=x$, we will get exactly the same graph. The function $g(x)$ is its own inverse.