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.