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=(20)/(-10) \\ m=-2 \end{gathered}`

Answer:

m = -2