QC & DA Question pg. 41, Formulas

[jbhm]

There's a confusing sample question in the QA&DA book on the bottom of page 41. The question states:

v&=2v-1

Then the question asks you to compare the values of (v&)& and 4v.

First we evaluate (v&)&

(v&)& = (2v-1)&

Then if we distribute that we get

2v& - &

and since we know v& = 2v-1 we can plug that in again yielding:

2(2v-1) - &

This is where I get lost. Somehow in the book they come up with:

2(2v-1) - 1

Would someone please help me with this? Thanks in advance!

[rheyn]

Hmm, error? Wouldn't be the first one....

[tommywallach]

Hey Guys,

Not an error at all. I think you're missing what kind of question this is. This is a function question (as the chapter should have said!).

That means that the funny symbol is representing a FUNCTION, not a VARIABLE. Remember f(x) = blah blah? This is just like that, but instead of saying f(x), they use a funny symbol. This is very common on the GRE, which knows we're all used to f(x), so it likes to switch things up.

So, to evaluate this, we need to run the function twice: (v&)&

(2v - 1)& -- This means that (2v-1) becomes our new v in the new function

(2v - 1)& = 2(2v-1) - 1 = 4v - 3

So we know this is smaller than 4v, because we are subtracting three.

Compound functions like this are quite common on the GRE. Here's another example, using the form you're more used to:

f(x) = x ^ 2

What is f(f(x))?

So now we need to take f(x^2), which means we plug x^2 in for x in the function (x^2)^2 = x^4.

Does this make sense?

-t

[jbhm]

Got it. Thanks a lot!

[tommywallach]

Glad to help!

-t

[manigraja100]

Hi Tommy,
Thanks for your explanation. How can i differentiate between a function question and a normal variable question ? just by the strange symbols in them or ?

[tommywallach]

Hey Mani,

Yeah, they'll always use either the f(x)/g(x)/h(x) format, or a VERY weird symbol (one that doesn't actually exist). In my experience, is always very obvious.

-t