## Calculus 8th Edition

Yes, $f \circ g$ is linear. The slope of $f \circ g$ is $m_1m_2$.
$$(f \circ g)(x)= f(g(x))=m_1(m_2x++b_2)+b_1$$ $$=m_1m_2x+m_1b_2+b_1$$The composite function $f \circ g$ is linear since it is of the form $mx+b$, with $m=m_1m_2$ and $b=m_1b_2+b_1$. The slope of the linear function $mx+b$ is $m$, so the slope of the composite function $f \circ g$ is $m_1m_2$.