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

1 Answer

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

Step-by-step 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

User Ross Mackay
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