Given that f(x)=3x+2 and g(x)=x^2-3x-6, find (gof)(6)

(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:

Now, we simplify:

Now, we plug in 6 into x and evaluate:

Thus, the value is 334

f

step-by-step explanation:

f

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)