Question

piecewise function:

f(x) = { (x+2)(x+1) / (x+1) if x does not = -1
{ a if x = -1

Determine the value of the constant a for which the function is continuous at x = -1.

Please explain to me how you got it! Thanks

Answer 1

\(\Large {(x+2)(x+1)\over(x+1) }\) is not defined when the denomininator \((x+1)=0\)

For any other x ... it behaves just like \(\Large {(x+2)\cancel{(x+1)}\over\cancel{(x+1)}}=x+2\)

so, at \(x=-1\), when \(f(x) = a =-1+2=\Large1\)... then the function is continuous.