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., f(x)=...) is thinking a little abstractly about what a function is. Basically, when you see f(x-1)=2x+3, you know that some combination of mathematical operations must happen to x-1 to transform it into 2x+3.

What could those operations be? Well, there’ll have to be some multiplication—that’s the only way we’re getting the x to turn into 2x. So let’s just start with that as an experiment; let’s say this function is just f(x)=2x and see what we’d get by plugging in x-1 as the argument:


Of course, that’s not exactly what we want, but it is close. All we need to do now is add 5 to turn -2 into +3. That tells us the function should really be f(x)=2x+5. Let’s just double-check:


Yep, that works! Once we know our function is f(x)=2x+5, all we need to do is drop -3 in there:



Leave a Reply