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 Question from Kenneth: f(x)=-x^2-6x find f(x-2)

Hi Kenneth,

I am going to illustrate with a different function.

Let $g(x) = 4x^3 - 7 x^2$ and find $g(2x - 1).$

The action of the function $g$ is described by the expression $g(x) = 4x^3 - 7 x^2.$ In this expression $x$ is the input to the function and the description says that you cube the input, multiply by 4 and then subtract 7 times the cube of the input. Hence if you input the number 5 then the cube of 5 is 125 so you multiply 125 by 4 and then subtract 7 times the square of 5. Hence

$g(5) = 4 \times 5^3 - 7 \times 5^{2} = 675.$

Likewise

$g(-2) = 4 \times (-2)^3 - 7 \times (-2)^2 = 60.$

If the input to the function $g$ is $2x-1$ then $g$ cubes the input to get $(2x-1)^{3},$ multiplies by 4 and then subtracts 7 times the square 0f the input. Hence

$g(2x - 1) = 4 \times (2x - 1)^3 - 7 \times (2x - 1)^{2}.$

I should expand and simplify the above expression.

Can you solve your problem now?
Penny