Answer:
(gof)(6) = 334
Step-by-step explanation:
The expression "(gof)(6)" means a composite function. Putting one function into another and then evaluating.
Thus,
(gof)(6) means "Put the function f into g and get a new function (gof)(x). Then put 6 into x of that new function and thus we get (gof)(6)"
So, let's find (gof)(x) first. Shown below:
[tex](gof)(x) = (3x+2)^2-3(3x+2)-6[/tex]
Now, we simplify:
[tex](gof)(x) = (3x+2)^2-3(3x+2)-6\\=9x^2+12x+4-9x-6-6\\=9x^2+3x-8[/tex]
Now, we plug in 6 into x and evaluate:
[tex](gof)(x)=9x^2+3x-8\\(gof)(6)=9(6)^2+3(6)-8\\(gof)(6)=334[/tex]
Thus, the value is 334
