Question

Am funcția f definita pe R cu valori in R, f(x)= x^4-2x^2+1. Cum demonstrez ca 0 <_f (x)<_1, oricare x apartine [-1, 1]?

Answer 1

x⁴-2x²+1=[(x-1)(x+1)]²=(x-1)²(x+1)²=(x²-1)²
(x²-1)²=0
x²-1=0
(x-1)(x+1)=0
x-1=0=>x=1
x+1=0=>x=-1
x∈[-1;1]