Select life tables Actuarial maths

Yes, but you do not write it as ([45]+2), you leave it as (47)

For life tables L(x) means the amount of people alive at time x. When using select it's slightly different, for select tables L([x]) is the amount of people alive at time x, who were also "evaluated" for insurance at time x. However the next year they don't become L([x+1]) as that would be the amount of people alive at time x+1, who were also "evaluated" for insurance at time x+1, so instead they become L([x]+1), which is the amount of people who were "evaluated" at x, and are now x+1.

For example lets say there are 2 people Adam and Bob. Adam and Bob are both 50, however only Adam is looking to buy insurance right now. Adam wants to buy life insurance and has to go through stuff like a questionnaire (does he smoke, drink, exercise, weight, age) and have some family history done (has anyone in his family suffered from heart disease, cancer etc). Because Adam has had these tests done at the age of 50, we now consider him to be select. So for Adam we use L([50]) and for Bob we use L(50).

The next year Adam and Bob are just doing whatever, the only important thing to note is Adam has NOT had another evaluation, he has simply bought insurance when he was 50 after having his evaluation. So now for Bob he is L(51), but for Adam he is L([50]+1) because he was evaluated at [50], but he is now 51 ([50]+1).

The next year Adam and Bob are doing whatever again, so now Bob is L(52) and Adam is L([50]+2). However we write Adam now as L(52) because our "select period" is 2 years, meaning after 2 years of your evaluation your mortality is the same as everyone else.

If you were to write in an exam something like L([50]+2) instead of L(52) for say AM92 you might get marks deducted/not counted based on how stringent the marking is.