Question

If f(x) is a function which is continuous everywhere, then we must have

Answer 1

$f(x)=\begin{cases}mx-17_{\text{ }}if_{\text{ }}x<-10{} \\ x^2+9x-7_{\text{ }}if_{\text{ }}x\ge-10{}\end{cases}$

Since the function is continuous everywhere we can conclude:

$\begin{gathered} x\ge-10 \\ f(-10)=(-10)^2+9(-10)-7=3 \\ x<-10 \\ f(-10)=3=-10m-17 \\ 3+17=-10 \\ 20=-10m \\ m=\frac{20}{-10} \\ m=-2 \end{gathered}$

Answer:

m = -2