Yes.
Find the numbers at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.
All three of these are continuous, so the only points where it cant be are the boundries. I plug in 0 for 6+x^2 and 7-x and the limits dont match. I do the same between 7-x and (x-7)^2 with 7 and get a see that is is continuous. Would x=0 be correct?