Finding a value that will make a function continuous

[shle]

Hi All, just a question regarding continuous functions.
From what I understand if x > 2, then any value of 'a' should make this function continuous? Any clarification would be very helpful!
Thanks in advance!

 

[pickslides]

Try 5(2)-1 = a(2)^2+1 solve for a

 

[shle]

Thank you, I get a = 2. Can you please explain to me the intuition behind that? Why is it that I have to use 5(2)-1 = a(2)^2+1 and solve for a?

 

[pickslides]

For the function to be continuous at x=2, then they must be equal at that point.