Question

Let f(x) = x2-3x and g(x) = x-3. Find and simplify a rule (expression) for (fog)(x). (DO NOT FACTOR YOUR ANSWER.)

Answer 1

$(f\circ g)(x)=x^2-9x+18$

Explanation

$\begin{gathered} f(x)=x^2-3x \\ g(x)=x-3 \end{gathered}$

Step 1

replace g(x) in f(x),where x

$\begin{gathered} f(x)=x^2-3x \\ (f\circ g)(x)=(x-3)^2-3(x-3) \end{gathered}$

Step 2

operate

remember:

$(a-b)^2=a^2-2ab+b^2$

Hence,

$\begin{gathered} (f\circ g)(x)=(x-3)^2-3(x-3) \\ (f\circ g)(x)=(x^2-2\cdot x\cdot3+3^2)-3(x-3) \\ (f\circ g)(x)=(x^2-6x+9)-3x+9 \\ (f\circ g)(x)=x^2-6x+9-3x+9 \\ (f\circ g)(x)=x^2-9x+18 \end{gathered}$

I hope this helps you