Question

If f(x) = x - 3, g(x) = 2x - 6, and h(x) = x^2 - 6x + 9, then (h - fg)(-1)=

Answer 1

The function h - fg is given by:

$\begin{gathered} (h-fg)(x)=h(x)-(fg)(x) \\ =h(x)-f(x)\cdot g(x) \end{gathered}$

Therefore,

$\begin{gathered} (h-fg)(x)=(x^2-6x+9)-(x-3)(2x-6) \\ =(x-3)^2-2(x-3)^2 \\ =-(x-3)^2 \end{gathered}$

Therefore,

$(h-fg)(-1)=-(-1-3)^2=-(-4)^2=-16$

Therefore,

(h - fg)(-1) = -16