True or False? The function \( f(x)=x^{3} \) and its inverse \( f^{-1}(x)=\sqrt[3]{x} \) are reflected over the line \( y=-x \). Option \#1: True Option \#2: False (1 point) The best answer is Option \#

False! The inverse function of \( f(x) = x^3 \) is indeed \( f^{-1}(x) = \sqrt[3]{x} \), but they are not reflected over the line \( y = -x \). Instead, they are reflections over the line \( y = x \). To visualize this, if you plot both functions, you’ll see that the points are symmetric concerning the line \( y = x \), not \( y = -x \). To understand the relationship between functions and their inverses, remember that a function and its inverse can be mirrored around \( y = x \). To find the inverse algebraically, swap the roles of \( x \) and \( y \) and solve for \( y \). This "mirroring" is a fundamental concept in function transformations!