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Francesca graphs the function f(x) = 2x - 3, George graphs the function g(x) = 4x2 – 2 – 1, and Harold graphs the function h(x) = 9(f(x)). Which function does Harold graph?
A. Oh(x) = 1622 - 50x + 38
B. Oh(x) = 8x3 - 142++3
c. Oh(x) = 8r2 - 2x - 6
D. Oh(x) = 4x2 - 12x +9

Respuesta :

JeanaShupp

Answer: A.  [tex]h(x)=16x^2-50x+38[/tex]

Step-by-step explanation:

Given: Francesca graphs the function  [tex]f(x) =2x - 3[/tex], George graphs the function [tex]g(x) = 4x^2 -x - 1[/tex].

Harold graphs the function [tex]h(x) = g(f(x))[/tex].

i.e. [tex]h(x)=g(2x - 3)[/tex]  [put value of f(x)]

[tex]=4(2x-3)^2-(2x-3)-1\\\\= 4((2x)^2-2(2x)(3)+3^2)-2x+3-1\ \ [(a-b)^2=a^2-2ab+b^2]\\\\= 4(4x^2-12x+9)-2x+2\\\\=16x^2-48x+36-2x+2\\\\=16x^2-50x+38[/tex]

So, Harold graph [tex]h(x)=16x^2-50x+38[/tex]

Hence, the correct option is A.  [tex]h(x)=16x^2-50x+38[/tex]

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