[tex]f(x)=\begin{cases}mx-17_{\text{ }}if_{\text{ }}x<-10{} \\ x^2+9x-7_{\text{ }}if_{\text{ }}x\ge-10{}\end{cases}[/tex]
Since the function is continuous everywhere we can conclude:
[tex]\begin{gathered} x\ge-10 \\ f(-10)=(-10)^2+9(-10)-7=3 \\ x<-10 \\ f(-10)=3=-10m-17 \\ 3+17=-10 \\ 20=-10m \\ m=\frac{20}{-10} \\ m=-2 \end{gathered}[/tex]
Answer:
m = -2
