To find the inverse of the function y = e^(-x^3), a logical first step is to take the natural logarithm of both sides, leading to x = -ln(y)^(1/3). For the function y = sin(1/x), it is noted that the function is not invertible due to its many-to-one nature, as multiple x-values can yield the same y-value. Specifically, the sine function has infinitely many solutions for y = 0, which complicates finding a unique inverse. In general, to find an inverse, one must solve for x in terms of y and ensure the function is one-to-one over the desired domain. Understanding these steps is essential for successfully determining the inverses of these functions.
