WILL GIVE MEDAL. You've learned about function notation in previous lessons, but could you use function notation to add two functions? How do you think you could simplify f(x) + g(x) if f(x) = 3x + 2 and g(x) = 4x? What about a function of a function such as f(g(x))? How do you think f(g(x)) could be simplified? What situations can you think of where combining functions would be useful?
May somebody help me with this with an example problem? I don't get this.
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okay we understand that
f(x) = 3x + 2
g(x) = 4x
so f(x) + g(x) would be?
oh i'm sorry, just saw that you'd like a different example question
f(x) = 5x + 3
g(x) = 7x
with this knowledge, what do you think f(x) + g(x) equals?
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I'm not sure what it would equal. This problem confuses me.
okay so, in the practice problem I gave you f(x) = 5x + 3 and g(x) = 7x. When there's a question such as f(x) + g(x) =, it's asking you what the values of f(x) and g(x) would equal with added together. So just substitute in their values. what would the equation look like then?
are you still having trouble?
Yes, I'm trying to work the problem out on some paper, but it's not really working out.
okay so if the value of f(x) is 5x + 3 we would replace f(x) with 5x + 3 in the equation
the equation would go from:
f(x) + g(x) =
5x + 3 + g(x) =
is that making more sense?
Yes. Okay, I going to guess here. Would that equal gx+5x+3?
*I'm* Whoops, stupid typos. Lol
gx+5x+3 is just the "new" equation. You still have to replace g(x) with it's value. What does g(x) =?
Hint: I gave it to you earlier
almost, g(x) = 7x
so the equation is not:
7x + 5x + 3
to simplify, you just add like terms. Like terms are the terms that resemble each other. In this case, the like terms would be?
Just to be clear, you're talking about simplifying g(x) = 7x, correct?
no, you have to simplify the equation as a whole.
Okay...I thought I had something going there for a second, but now I don't. May you simplify the expression for me? I keep getting it wrong.
okay so the like terms in the equation would be 5x and 7x
in the equation 7x + 5x + 3 is says we have to add them. (we don't know the value of x so we add the numbers) 7 + 5 is 12 so the equation is now:
12x + 3 =
f(x) + g(x) is 12x + 3
Yes, I think I'm understanding more now.
okay now moving on to the f(g(x)) problem. I'm going to use the same example values:
f(x) = 5x + 3
g(x) = 7x
in f(g(x)), the x in f(x) is being replaced by g(x). That means that in f(x) = 5x + 3, ALL Xs need to be replaced with the value of g(x). We know they value of g(x) is 7x, so now substitute the Xs in f(x) with that value