Respuesta :

ghanami
Hello here is a solution :
h(g(f(x))) ?

g(f(x))= g(2x+5)=(2x+5)²=(2x)²+2(2x)(5)+5² = 4x²+20x+25
h(g(f(x)))(x) = h(4x²+20x+25) = -2(4x²+20x+25) 
h(g(f(x)))(x) = -8x²-40x-50

Answer:

[tex]h(g(f(x)))(x) = -8x^2-40x-50[/tex]

Step-by-step explanation:

[tex]f(x) = 2x + 5[/tex]

[tex]g(x)=x^2[/tex]

[tex]h(x)=-2x[/tex]

[tex]h(g(f(x)))[/tex], first replace f(x) with 2x+5

[tex]h(g(2x+5))[/tex]

Replace 2x+5 for x in g(x). [tex]g(2x+5)=(2x+5)^2= (2x+5)(2x+5)= 4x^2+20x+25[/tex]

[tex]h(g(2x+5))[/tex] becomes [tex]h(4x^2+20x+25)[/tex]

Replace x with 4x^2+20x+25 in h(x)

[tex]h(4x^2+20x+25)=-2(4x^2+20x+25)=-8x^2-40x-50[/tex]