F(x)=x²/³ (6-x)²/³ =(x(6-x))²/³
x-1 x-1
1.
a) x-1≠0
x≠1
D(f)=(-∞; 1)U(1; +∞)
б) f(3-x)=((3-x)(6-(3-x))²/³ = ((3-x)(3+x))²/³ = (9-x²)²/³
3-x-1 2-x 2-x
f(3+x)=((3+x)(6-(3+x)))²/³ = ((3+x)(3-x))²/³ = (9-x²)²/³
3+x-1 2+x 2+x
(f(3-x)+f(3+x))³ = [ (9-x²)²/³ + (9-x²)²/³]³ = [(9-x²)²/³ (2+x) + (9-x²)²/³ (2-x)]³ =
[ 2-x 2+x ] [ (2-x)(2+x) ]
= [ (9-x²)²/³ (2+x+2-x)]³ = 4³ (9-x²)²
[ 4-x² ] (4-x²)³
При х=2√3
4³ (9-(2√3)²)² = 64 (9-12)² = 64 * (-3)² = 64*9 = -9/8
(4-(2√3)²)³ (4-12)³ (-8)³ (-8)² * (-8)