Tip:
Highlight text to annotate it
X
Hi, I'm Kendall Roberg, and today we are going to perform operations on functions.
We have 2 functions, f and g.
f in terms of x is defined as -x + 4.
g of x is 2x + x^2.
So what would happen if we added these two functions together?
Well, let's see.
f(x) + g(x), we can rewrite this as...since f(x) is just -x + 4 let's just write -x +4...
And we're going to add that to g(x), which is 2x + x^2.
Now all we have to do is combine like terms and we're done.
So x^2...2x minus an x is gonna be x...and 4.
So f(x) + g(x) is x^2 + x + 4.
What about f(x) - g(x)?
Now in this situation, you write f(x) again...
and we're subtracting g(x).
Now I drew the parentheses here to remind me that I'm subtracting this entire thing, not just the 2x.
I'm subtracting 2x + x^2.
So combining like terms again, we're left with -x^2...-x minus 2x would be -3x...and plus 4.
Alright...now the next one, problem 3, asks us what is f(x) times g(x).
And in this situation, we're going to say (-x + 4), which is f(x), times (2x + x^2).
We have two binomials being multiplied, so we're going to have to use FOIL, and it looks like we get a -2x^2 - x^3 + 8x + 4x^2.
Combining like terms and rearranging so we're in decreasing exponent order, we have -x^3 + 2x^2 + 8x.
I'll go ahead and circle that so you see what the final answer is.
f(x) times g(x) is -x^3 + 2x^2 + 8x.
Now the last problem will ask us to divide f(x) by g(x).
So we're going to make a fraction, and in the numerator of the fraction, we're going to write f(x), or -x + 4, and in the denominator of the fraction, we're going to write g(x), or 2x + x^2.
Now, because there's no common monomial we can factor out of either of these, we actually can't reduce that; that's our final answer.
And that's how you form operations with functions.