Question

If f(x) = 3x - 1, g(x) = 6x-2, and h(x) = 9x² - 6x + 1, then(f- g)(-3) =

Answer 1

Solution:

Given the functions below

$\begin{gathered} f\mleft(x\mright)=3x-1 \\ g\mleft(x\mright)=6x-2 \\ h\mleft(x\mright)=9x²-6x+1 \end{gathered}$

The composite function will be

$\begin{gathered} (f-g)(x)=(3x-1)-(6x-2)=3x-1-6x+2= \\ Collect\text{ like terms} \\ (f-g)(x)=3x-6x-1+2=-3x+1 \\ (f-g)(x)=-3x+1 \end{gathered}$

Where x = -3,

$\begin{gathered} (f-g)(x)=-3x+1 \\ (f-g)(-3)=-3(-3)+1=9+1=10 \\ (f-g)(x)=10 \end{gathered}$

Hence, the answer is 10