To evaluate, first evaluate and then plug in that answer into . Thus,

Then, is

and .

To find we plug in the function everywhere there is a variable in the function .

This is the composition of "f of g of x".

Foil the square and simplify:

Replace and substitute the value of into so that we are finding .

and is read as "g of f of x" and is equivalent to plugging the function f(x) into the variables in the function g(x).

Finding is the same as plugging in into much like one would find for a function .

and

Insert g(x) into f(x) everywhere there is a variable in f(x):

When doing a composition of functions such as this one, you must always remember to start with the innermost parentheses and work backward towards the outside.

So, to begin, we have

.

Now we move outward, getting

.

Finally, we move outward one more time, getting

.

To solve, plug 1 into g and then your answer into f.

Thus,

Plugging in this value into our f function we get the final answer as follows.

To solve, simply plug in 2 into f and then the result into g.

Thus,

g(f(x)) simply means replacing every x in g(x) with f(x).

After simplifying, it becomes

Given and , find .

Begin by breaking this into steps. I will begin by computing the step, because that will make the late steps much more manageable.

Next, take our answer to and plug it into .

So we are close to our final answer, but we still need to multiply by 3.

Making our answer 84.