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`

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`