Răspuns:
h(x)=2x-1
l(x)=[tex]x^{2} -1[/tex]
g(x)=3[tex]x^{2}[/tex]
f(x)=x-2
2)h o l = h ( l (x) ) = h([tex]x^{2} -1[/tex])= 2( x^2-1) -1 = 2x^2 -2-1 = 2x^2 -3
l o h = l (h(x))= l ( 2x-1) =( 2x-1) ^2 -1 = 4x^2 - 4x +1 -1 = 4x^2 - 4x= 4x(x-1)
h o h = h(h(x))= h( 2x-1) = 2(2x-1) -1 = 4x -2 -1 =4x -3
l o l = l(l(x)) = l( x^2-1) = [tex](x^{2} -1)^{2}[/tex] -1 = x^4-2x^2 +1 -1 = x^4-2x^2 = x^2( x^2-2)
3) f o h o g = f ( h ( g ( x ) ) ) = f(h ( [tex]3x^{2}[/tex]) ) = f( 2(3x^2) -1 )= f( 6[tex]x^{2}[/tex] -1 ) = (6x^2-1)^2-1=36x^4-12x^2+2 -1 =36x^4-12x^2+1= 12x^2(3x^2-1) +1
h o g o h o l= h(g(h(l(x))) = h(g(h([tex]x^{2} -1[/tex])))= h(g( 2(x^2-1) -1)=
h(g([tex]2x^{2}[/tex]-3)= h( 3([tex]2x^{2} -3[/tex]))= h( [tex]6x^{2}[/tex] -9)= 2([tex]6x^{2} -9[/tex])-1= [tex]12x^{2} -18-1=12x^{2} -19[/tex]
