Question

responde ai gente.... 99 pontos!

função composta, sendo g(x)= 4² + 2 e  h (x) = 3x +5,  calcule: 
a) g(h(x))
b)h(g(x))
c)g(g(x))
d)h(h(x))
e) g(h(4)) + h (g(4))

Answer 1

$g(h(x)) = 4(h(x))^{2} + 2 = \\\\ g(h(x)) = 4(3x + 5)^{2} + 2 = \\\\ g(h(x)) = 4(9x^{2} + 30x + 25) + 2 = \\\\ \boxed{g(h(x)) = 36x^{2} + 120x + 102}\\\\ h(g(x)) = 3x + 5 =\\\\ h(g(x)) = 3(g(x)) + 5 =\\\\ h(g(x)) = 3(4x^{2} + 2) + 5 =\\\\ h(g(x)) = 12x^{2} + 6+ 5 =\\\\ \boxed{h(g(x)) = 12x^{2} + 11}\\\\ g(g(x)) = 4x^{2} + 2 = \\\\ g(g(x)) = 4(4x^{2} + 2)^{2} + 2 = \\\\ g(g(x)) = 4(16x^{4} + 16x^{2} + 4) + 2= \\\\ \boxed{g(g(x)) = 64x^{4} + 64x^{2} + 18}\\\\ h(h(x)) = 3x + 5 = \\\\ h(h(x)) = 3(3x + 5) + 5 = \\\\ \boxed{h(h(x)) = 9x + 20 }\\\\[tex] [tex]g(h(x)) + h(g(x)) = 36x^{2} + 120x + 102 + 12x^{2} + 11=\\\\ g(h(x)) + h(g(x)) = 48x^{2} + 120x + 113 = \\\\ g(h(4)) + h(g(4)) = 48.4^{2} + 120.4 + 113 = \\\\ g(h(4)) + h(g(4)) = 768 + 480 + 113\\\\ \boxed{g(h(4)) + h(g(4)) = 1361}$