Răspuns:
Explicație pas cu pas:
E(x) = [1-1/(x+1)]·[(x+1)/(x²+1)]:[(x+3)/(4x-4) - ⁴⁾1/(x-1)]
E(x) = [(x+1-1)/(x+1)]·[(x+1)/(x²+1)]:[(x+3-4)/(4x-4)]
E(x) = [x/(x²+1)]:[(x-1)/4(x-1)]
E(x) = [x/(x²+1)]·4
E(x) = 4x/(x²+1) ; ∀ x ∈ R-{±1}
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-2 ≤ E(x) ≤ 2 <=>
-2 ≤ 4x/(x²+1) ≤ 2 <=>
-2(x²+1) ≤ 4x ≤ 2(x²+1) =>
4x + 2(x²+1) ≥ 0
4x - 2(x²+1) ≤ 0
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4x +2x²+2 ≥ 0 <=> x²+2x+1 ≥ 0 <=> (x+1)² ≥ 0 , adevarat pt. ∀ x ∈ R-{±1}
4x - 2x²-2 ≤ 0 <=> 2x²-4x+2 ≥ 0 <=> x²-2x+1 ≥ 0 <=>
(x-1)² ≥ 0 , adevarat pt. ∀ x ∈ R-{±1} =>
-2 ≤ E(x) ≤ 2
