Find g(f(x)) and f(2g(x))

Question

where f(x)=2x^2-1 and
g(x)= the absolute value of x-1

Answer 1

g(f(x))= |2x^2 - 2| = 2|x^2 -1|

That assumes that g(x) = |x-1|, not |x| -1. The way you wrote it is ambiguous.