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Math Help - linear functions!!

  1. #1
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    linear functions!!

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

    Is fog also a linear function? if so, whats the slope?
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  2. #2
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    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?
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  3. #3
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    Re: linear functions!!

    Quote Originally Posted by Prove It View Post
    \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.
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  4. #4
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    Re: linear functions!!

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