Think of it this way: the *g* function is doing SOME AS-YET-UNKNOWN THINGS to (–*x* + 7) to turn it into (2*x* + 1). Of the simple mathematical operations probably at play here (addition, subtraction, multiplication, division) what could be going on?

First, the only way you go from –*x* to 2*x* is you multiply by –2. So let’s see what happens if we just multiply *f*(*x*) by –2.

**–2**(–*x* + 7) = 2*x* – 14

OK, so the first part’s good now, but how can we turn –14 into +1? Well, we don’t want to multiply or divide again because that would screw up the 2*x* we just nailed down, so why don’t we try adding 15?

2*x* – 14 **+ 15** = 2*x* + 1

Combine the two operations we just did (multiply by –2, add 15) and you have the *g* function. The function *g* will multiply its argument by –2, then add 15. Mathematically, we can write that like this:

*g*(*x*) = –2*x* + 15

Now, start from the top and make sure we’re right.

* g*(*f*(*x*))

= *g*(–*x* + 7) <– substitute (–*x* + 7) for *f*(*x*)

= –2(–*x* + 7) + 15 <– apply the *g* function to (–*x* + 7)

= 2*x* – 14 + 15

= 2*x* + 1

It works! Now all we need to do is calculate *g*(2).

*g*(2) = –2(2) + 15

*g*(2) = 11

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