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Verified Answer :

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:

\(h(g(f(x)))(x) = -8x^2-40x-50\)

Step-by-step explanation:

\(f(x) = 2x + 5\)

\(g(x)=x^2\)

\(h(x)=-2x\)

\(h(g(f(x)))\), first replace f(x) with 2x+5

\(h(g(2x+5))\)

Replace 2x+5 for x in g(x). \(g(2x+5)=(2x+5)^2= (2x+5)(2x+5)= 4x^2+20x+25\)

\(h(g(2x+5))\) becomes \(h(4x^2+20x+25)\)

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

\(h(4x^2+20x+25)=-2(4x^2+20x+25)=-8x^2-40x-50\)

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