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Evaluating composite functions: using tables

Given tables of values of the functions f and g, Sal evaluates f(g(0)) and g(f(0)).

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• I really, really don't get this. And I can't graduate unless I get through Algebra 2. How does the graph stuff make up an equation?
• Sal is showing that f(x) and g(x) represents equations. We don't know what those equations are, instead we are only given their inputs and outputs.
So, for f(x) when x= -1 the output is 5. In other words: f(-1)=5

In the question above f(g(0)) means we are given 0 as an input for g(x), the output is 5, we then have f(5), the output of g(0) becomes the input for f(x), then the output of f(5)=11

Does that make any more sense?
• Hi, what if you are asked for something like this:

Two functions f and g are such that f(x)=1+2x and g(f(x))=x+3. What is the value of g(5)?

• Your function g(x) is defined as a combined function of g(f(x)), so you don't have a plain g(x) that you can just evaluate using 5. The 5 needs to be the output from f(x). So, start by finding: 5=1+2x
That get's you back to the original input value that you can then use as the input to g(f(x)).

Subtract 1: 4=2x
Divided by 2: x=2

Now, use 2 as the input to g(f(x))=2+3 = 5

I think this is right. Maybe someone else can verify it.
• I want to know how to solve f(x) and g(x) using a table without a value, like in this video it shows 0, i want to solve without any value.
• For that you need to know f(x) and g(x) in terms of x(like f(x)=3x+ln(x) for example) so that you can evaluate them at any value.
In the type of questions where f(x) and g(x) are not given in terms of x, the table of values must be used to evaluate them and their composite functions. This can only be done at the x values given in the table.
(1 vote)
• So I hope someone can understand this without actually seeing the tables I'm working with but here's a problem I'm stumped on:
"make a table of values for f(x) after the given translation: 3 units up."
It then gives me a table with a column "x" and a column "f(x)" with functions in both. then there is an empty column I'm supposed to fill in with the name "g(x)". So, what is the process to complete the function with the criteria of "3 units up"? Can one of you that are actually smart help me out please?
• I'm not certain but I think "3 units up" could mean either of these 2 things :-
1. The graph of f(x) has been vertically moved up in the y axis by 3. You have to find the new line & from there get the outputs for the empty column.
2. It could be asking for f(x+3) in which case find the equation for f(x) & substitute all the x in the equation with x+3.
• Hi there, can someone tell me what level of math this is (e.g. what high school grade level (grade 10/11/12? or AP)? Many thanks!
• It depends on the country. If you are asking about the US, then it depends on the state. I learned this in 7th grade when I took Algebra I, but it is possible to not reach it until maybe 10th or even 11th grade depending on several factors.
• What if it asks you F x G (-3)
• That is simply another way of saying f(g(3)). Supposing the equations are f(x)=x^2 + 3 and g(x)=1+x-6;
g(3)=1+3-6
g(3)=4-6
g(3)=-2
Now that you know g(3) is equal to -2, you know that f(g(3)) is equal to f(-2). So,
f(-2)=-2^2+3
f(-2)=4+3
f(-2)=7
Hope this helps!
• okay so im working on this math AIR packet and one question is

Ryan works for a delivery service. The function f(n) is used to calculate his daily pay, in dollars, on a day when he makes (n) deliveries
f(n)=7n+96
and the table gives me the first two numbers of deliveries which is 0 and
5
and I figured out the daily pay for both, for f(0)=96 and f(5)=277 and it only gives me the daily pay after that and I don't know how to figure out the number of deliveries
• Set the daily pay equal to 7n + 96 so you can solve for n
N= number of deliveries
(1 vote)
• (x) F(x) G(x)
-2 1
0 -1
1 -4
3 -3 This is what my tables look like.