10. Correct. The answer is true
Since y = x4 + 1 the relationship between the values y and x of the random variables y and x is given by:
y = x4+1 or x = (y-1)1/4, where y = 2, 17, 82, etc.
and the real positive root is taken. Then the required probability function for y is given by
g(y) = 2-(y-1)^(1/4) y = 2, 17, 82, etc.
g(y) = 0 otherwise
using Theorem 2-1, p.44 in Schaum's Outlines Probability and Statistics.