Think of it this way: the g function is doing SOME AS-YET-UNKNOWN THINGS to (–x + 7) to turn it into (2x + 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 2x is you multiply by –2. So let’s see what happens if we just multiply f(x) by –2.

–2(–x + 7) = 2x – 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 2x we just nailed down, so why don’t we try adding 15?

2x – 14 + 15 = 2x + 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) = –2x + 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)
= 2x – 14 + 15
= 2x + 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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