Would you please work #10 in section 3 of PSAT Test 1?

Sure. For me, the trick to solving questions where the function isn’t defined the simplest way (e.g., ) is thinking a little abstractly about what a function is. Basically, when you see , you know that some combination of mathematical operations must happen to to transform it into .

What could those operations be? Well, there’ll have to be some multiplication—that’s the only way we’re getting the to turn into . So let’s just start with that as an experiment; let’s say this function is just and see what we’d get by plugging in as the argument:

Of course, that’s not *exactly* what we want, but it is close. All we need to do now is add to turn into . That tells us the function should really be . Let’s just double-check:

Yep, that works! Once we know our function is , all we need to do is drop in there: