Question

exercitile 2 si 3 din poza

Answer 1

Răspuns:

h(x)=2x-1

l(x)=$x^{2} -1$

g(x)=3$x^{2}$

f(x)=x-2

2)h o l = h ( l (x) ) = h($x^{2} -1$)= 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) = $(x^{2} -1)^{2}$ -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 ( $3x^{2}$) ) = f( 2(3x^2) -1 )= f( 6$x^{2}$ -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($x^{2} -1$)))= h(g( 2(x^2-1) -1)=

h(g($2x^{2}$-3)= h( 3($2x^{2} -3$))= h( $6x^{2}$ -9)= 2($6x^{2} -9$)-1= $12x^{2} -18-1=12x^{2} -19$