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(male narrator) In this video,
we will look at the four basic operations
that we can do with functions.
This is mostly getting used to the new notation
where when we see f plus g of x, this simply means take f of x
and add to it whatever g of x is.
Similarly, if we see subtraction between the f and g,
that means take the first function
and subtract the second function.
We can also multiply f of x times g of x,
and we can divide
f of x by g of x
using the similar notation.
Let's take a look at some examples
where we actually work out these operations
with two involved functions.
In this problem,
we start with f plus g of -2.
This means we have to find f of -2;
and then, we will find g of -2;
and then, we will add the results together.
First, let's look at f: f of -2 simply means
we replace the x with -2 to get -2 minus 4, or -6;
g of -2 means we plug -2 in the g function
to get -2 squared, minus 6 times -2, plus 8,
as we replace each of the x's with -2.
Notice -2 squared is 4, plus -6 times -2 is 12, plus 8,
and we end up with a total of 24.
Now, we're asked to add these two results together,
meaning we're gonna take the -6 from the f function
and add 24 from the g function to get 18:
f plus g of -2 is equal to 18.
Let's try a subtraction problem.
First, plug in 3 into the f equation:
f of 3 means we plug 3 into f, giving us 3 minus 4, or -1.
Plug in 3 into the g function
gives us 3 squared, minus 6 times 3, plus 8.
Or multiplying, 9 minus 18 plus 8 is equal to -1.
This function asks us to subtract these two results:
-1 from f; minus -1 from g; and when we add the opposite,
we find out f minus g of 3 is 0.
Let's find out what f times g of 1 is.
This means, we plug 1 into the f function,
giving us 1 minus 4, which is -3.
And also, we're gonna plug 1 into the g function,
giving us 1 squared, minus 6 times 1, plus 8;
or 1 minus 6 plus 8, which is 3.
This notation wants us
to multiply the answers together:
-3 times 3 is equal to -9.
The only operation left to consider is division.
This time, plugging 0 into the f equation:
f of 0 is 0 minus 4, or -4;
g of 0 is equal to x squared,
or 0 squared;
minus 6 times 0; plus 8.
Working this out,
we can see the answer is 8.
Here, we are asked
to divide these two answers:
f over g,
-4 over 8 reduces to -1/2.
In this way, we can use this notation
for addition, subtraction, multiplication, and division
to plug a number into both functions,
and then do the operation with the results.
We can also do this at a variable value,
and this is what we will consider
in Part 2 of this video.