Question

find the value of b and c such that the function f(x) is continuous on the entire real line

f(x) = x+1 , 1= 1

Answer 1

I know how to do it if it was only one constant that I needed to find
but with 2 where do I get the second equation from and how do I know which condition to apply ?

Answer 2

you have two limits you can plug in
$$
\large{
\lim_{x \to 1} ~x+1 = \lim_{x \to 1} ~x^2 +bx + c
\\
\lim_{x \to 3} ~x+1 = \lim_{x \to 3} ~x^2 +bx + c


}$$

Answer 3

we have to apply these condions:
at x= 1:
\[f\left( 1 \right) = 1 + 1 = 2 = 1 + b + c\]
whereas at x=3:
\[f\left( 3 \right) = 3 + 1 = 4 = 9 + 3b + c\]

Answer 4

but why is it okay to use x=1 for the x2+bx+c part ?