1. **State the problem:** We are given two functions $f(m) = 8m + 7$ and $g(m) = 5m - 6$. We need to find the values of the compositions $(f \circ g)(-3)$ and $(g \circ f)(-3)$. 2. **Recall the definition of composition:** - $(f \circ g)(x) = f(g(x))$ means we first apply $g$ to $x$, then apply $f$ to the result. - $(g \circ f)(x) = g(f(x))$ means we first apply $f$ to $x$, then apply $g$ to the result. 3. **Calculate $(f \circ g)(-3)$:** - First find $g(-3)$: $$g(-3) = 5(-3) - 6 = -15 - 6 = -21$$ - Now find $f(g(-3)) = f(-21)$: $$f(-21) = 8(-21) + 7 = -168 + 7 = -161$$ 4. **Calculate $(g \circ f)(-3)$:** - First find $f(-3)$: $$f(-3) = 8(-3) + 7 = -24 + 7 = -17$$ - Now find $g(f(-3)) = g(-17)$: $$g(-17) = 5(-17) - 6 = -85 - 6 = -91$$ **Final answers:** $$(f \circ g)(-3) = -161$$ $$(g \circ f)(-3) = -91$$