Question

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

Answer 1

Answer: A.  $h(x)=16x^2-50x+38$

Step-by-step explanation:

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

Harold graphs the function $h(x) = g(f(x))$.

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

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

So, Harold graph $h(x)=16x^2-50x+38$

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