**Register for an Upcoming Free GRE Webinar**

Reserve your spot now!

Reserve your spot now!

# Additional Algebra I and II topics

**23**

Let the function f be defined by f(x)=x+6. If 3f(n) = 39. what is the value of f(2n)?

I've asked about a problem like this before...this question is wording it differently because it's asking for the value of f(2n). I tried backplugging but then realized that I can't divide the f(2n) by 2 because it is inside the parentheses. Also figured out that f(n)=13.

Thanks!

#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

#### In this Discussion

Before you post, please remember:

**Search for your topic**. A discussion may already be waiting for you!

**Focus on one topic per post**. For example, ask about just one practice exercise rather than two or more in a single post.

**Don’t post copyrighted material**. For example, don't post practice exercises from books or courses that must be purchased. Even some free stuff, including from ETS, may be copyrighted and so shouldn't be posted.

## Posts

97This problem requires some algebra but can also be solved using problem solving techniques, in this case Backplugging.

Let's take a look. Remember that the first thing to do with functions is to get the function by itself. You can manipulate equations with functions in the same manner in which you'd handle any other algebraic function.

Since you're starting with 3

f(n) = 39, you want to start by isolatingf(n). Divide both sides by 3. You end up withf(n) = 13.You now have two possible paths to the solution.

## Pure Algebra

Record What You Know™f(x) = x + 6f(n) = 1313 = n + 6

n = 7

f(2n) =f(14) = 14 + 6 = 20## Backplugging

Record What You Know™f(x) = x + 6f(n) = 13 = n + 6n = 7

…

f(2n) = … ??? = 2n + 6 …… Solve for n … Does n = 7?(A)

(B)

(C) 20 ……… 20 = 2n + 6 …… n = 7 ………… YES! we've found the answer

(D)

(E)

I hope this helps!