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# Calculus/Composite functions

Question
I am currently learning about composite functions,  My text book has the following problem : (fofg)(x) where f(x)=x^2+3x-1 and g(x)=2x-3.  The answer the book is giving me is 4x^2+12x+9+6x+9-1.  Where does the 12x come from?

Is (fofg)(x) really suppose to be (fog)(x)?

What that means is to take g(x) and put it in as the x's in f(x).

It seems clearer to say that f(y) = y²+3y-1 and g(x) = 2x-3.
What (fog)(x) is can be found by finding f(y) where y = g(x).
In other words, take y = 2x - 3.

With y = 2x - 3 put into y²+3y-1 gives (2x-3)²+3(2x-3)-1.
Now (2x-3)² is 4x² - 12x + 9 and -3(2x-3) is -6x + 9.

Putting both of these terms into  (2x-3)² + 3(2x-3) - 1 gives 4x² - 12x + 9 - 6x + 9 - 1.

To me it looks like a misprint, for to get this answer, we need g(x) = 2x + 3
{note the '+ 3' instead of the '- 3'}.  That would make the -12x into +12x and the -6x into +6x.

Note that the x terms can be combined, since -12x - 6x = -18x { or 12x + 6x = 18x}.
Also, the constants can be combined, since 9 - 1 = 8.
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