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:
