The solution of f(E) is not right because 1≤ y≤ 1/4 would imply the set (-∞,1/4] U [1,∞). But, f(1.5) = 0.444 ∉ (-∞,1/4] U [1,∞) whereas 1.5 satisfies x ∈ [1,2]. Therefore f(E) is derived as follows:
f(E)= f{x∈ [SIZE="3"]ℝ : 1≤ x ≤ 2}
Now, 1≤ x ≤ 2 ⇔ 1≥ 1/x ≥ 1/2 ⇔ 1≥ 1/x^2 ≥ 1/4 ⇔ 1≥ y...