1. ## linear functions!!

f(x)= m1x+b1 g(x)=m2x+b2

Is fog also a linear function? if so, whats the slope?

2. ## Re: linear functions!!

\displaystyle \begin{align*} f(x) = m_1x + b_1 \end{align*} and \displaystyle \begin{align*} g(x) = m_2x + b_2 \end{align*}. Then we have

\displaystyle \begin{align*} f \circ g(x) &= f\left(g(x)\right) \\ &= m_1\left(m_2x + b_2 \right) + b_1 \\ &= m_1m_2x + m_1b_2 + b_1 \end{align*}

If you call \displaystyle \begin{align*} m = m_1m_2 \end{align*} and call \displaystyle \begin{align*} b = b_1 \end{align*}, then you will have \displaystyle \begin{align*} mx + b \end{align*}, which is linear. What's its slope?

3. ## Re: linear functions!!

Originally Posted by Prove It
\displaystyle \begin{align*} f(x) = m_1x + b_1 \end{align*} and \displaystyle \begin{align*} g(x) = m_2x + b_2 \end{align*}. Then we have

\displaystyle \begin{align*} f \circ g(x) &= f\left(g(x)\right) \\ &= m_1\left(m_2x + b_2 \right) + b_1 \\ &= m_1m_2x + m_1b_2 + b_1 \end{align*}

If you call \displaystyle \begin{align*} m = m_1m_2 \end{align*} and call \displaystyle \begin{align*} b = b_1 \end{align*}, then you will have \displaystyle \begin{align*} mx + b \end{align*}, which is linear. What's its slope?
Well, actually you want $b= b_1+ m_1b_2$.

4. ## Re: linear functions!!

Originally Posted by HallsofIvy
Well, actually you want $b= b_1+ m_1b_2$.
Cut me some slack, it was 4am when I posted :P