Walk through examples, explanations, and practice problems to learn how to find and evaluate composite functions.

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Tess Van Horn

9 years agoPosted 9 years ago. Direct link to Tess Van Horn's post “In practice Q 4, where is...”

In practice Q 4, where is 4t created? I see where t^2 and 4 come from, but am not sure what puts 4t in

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(69 votes)

Mr.Magroo

9 years agoPosted 9 years ago. Direct link to Mr.Magroo's post “I was stuck on this too, ...”

I was stuck on this too, but I think the reason is that (t-2)^2 = (t-2)(t-2) . Using the distributive property, you get t^2-4t+4.

(133 votes)

Nigar Kainath

8 years agoPosted 8 years ago. Direct link to Nigar Kainath's post “(f ∘ g)(x)here, what doe...”

(f ∘ g)(x)

here, what does the sign ∘ mean?•

(2 votes)

Levi Geadelmann

8 years agoPosted 8 years ago. Direct link to Levi Geadelmann's post “(f ∘ g)(x) is read "f of ...”

(f ∘ g)(x) is read "f of g of x", so the ∘ translates to "of".

In this case, if you had functions defined, f(x) and g(x), then to get (f ∘ g)(x) you would substitute g(x) for x inside of f(x). Another way to write it is f(g(x)).(18 votes)

Rory Avera

8 years agoPosted 8 years ago. Direct link to Rory Avera's post “How do you know when to u...”

How do you know when to use the "inside out property" or the composing function?

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(9 votes)

Judith Gibson

8 years agoPosted 8 years ago. Direct link to Judith Gibson's post “It doesn't really matter ...”

It doesn't really matter --- they will both give the same answer, so it's up to you to choose what works best/easiest for you with the problem you're given at the time!

(But, of course, you need to be familiar with both techniques.)(7 votes)

Aditya Mahajan

5 years agoPosted 5 years ago. Direct link to Aditya Mahajan's post “May someone please explai...”

May someone please explain the challenge problem to me?

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(4 votes)

Dylan Chan

5 years agoPosted 5 years ago. Direct link to Dylan Chan's post “The challenge problem say...”

The challenge problem says, "The graphs of the equations y=f(x) and y=g(x) are shown in the grid below." So basically the two graphs is a visual representation of what the two different functions would look like if graphed and they're asking us to find (f∘g)(8), which is combining the two functions and inputting 8. From the definition, we know (f∘g)(8)=f(g(8)). So let's work "inside out". If we look at the graph of "g", we see that g(8) is 2 (look at the 8 at the x-axis and if you go up to where it meets the line, the y value would be 2). Because g(8)=2, then when you substitute it back in the equation, f(g(8)) would equal f(2). Then if we look at the graph of "f", we can see that f(2) is -3. (when you look at the 2 in the x-axis, it will correspond to -3 on the y-axis). So by looking at the graph, you can figure out that (f∘g)(8) is approximately -3.

~Dylan(15 votes)

flowermap21

a year agoPosted a year ago. Direct link to flowermap21's post “In question 4 how do peop...”

In question 4 how do people get the 4t in tsquered-t4+9?

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(3 votes)

Kim Seidel

a year agoPosted a year ago. Direct link to Kim Seidel's post “It comes from (t-2)^2(t-...”

It comes from (t-2)^2

(t-2)^2 = (t-2)(t-2) = t^2-2t-2t+4 = t^2-4t+4

To square binomials, you need to use FOIL or the pattern for creating a perfect square trinomial. You can't square the 2 terms and get the right answer.Hope this helps.

(11 votes)

Ceaseless_Thoughts

a year agoPosted a year ago. Direct link to Ceaseless_Thoughts's post “in the example question "...”

in the example question "g(x)= x+4, h(x)= x(squared)-2x" how does it get the +8x and -2x in the distribute section ?

here's the distribute equation =(x(squared)+8x+16−2x−8)

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(5 votes)

Kim Seidel

a year agoPosted a year ago. Direct link to Kim Seidel's post “h(g(x)) = (x+4)^2 - 2(x+4...”

h(g(x)) = (x+4)^2 - 2(x+4)

Basically each "x" in h(x) gets replaced with (x+4), which if g(x). Then, you simplify.1) FOIL out (x+4)^2:

h(g(x)) = x^2+4x+4x+16 - 2(x+4) = x^2 + 8x + 16 - 2(x+4)2) Distribute -2: h(g(x)) = x^2 + 8x + 16 - 2x - 8

3) Combine like terms: x^2 + 6x + 8

Hope this helps.

(6 votes)

ScribofThoth

a year agoPosted a year ago. Direct link to ScribofThoth's post “I still can't get this. I...”

I still can't get this. I think my problem is them showing multiple ways to do this instead of focusing on how to combine it into one equation. Either I have to work each function alone then combine them at the end or have more help figuring out how to make one equation.

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(2 votes)

ersepsi

a year agoPosted a year ago. Direct link to ersepsi's post “I don't think their aim i...”

I don't think their aim is to show you the multiple ways you can evaluate the composite function.

The first example they basically show what evaluating a composite function really means, it's like you said "work each function alone". In the second example they showed a more faster and efficient way to evaluate the composite function by combining them into one equation.

If you're still confused about composite functions, I'll explain this way:

we have a function f(x), this function takes "x" as "input". Now, I'm certain you're used to the variable x being substituted for a number, but in maths, you can pretty much substitute it for anything you like. (Expressions for example)

Like I can let x = 5, but I can also let x = 2h. Doesn't that mean I can also substitute x for some function? In other words x = g(x).

Say if g(k) = 4k, then this would become: x = 4k. (Because x = g(k) = 4k)

Since we let x = g(k) = 4k, then our function f can be written as: f( g(k) ) or f(5k) (We substituted x for g(k) )

if f(x) = 5x, by substituting x for g(k), this becomes:

f( g(x) ) = 5g(x) ---> f( 4k ) = 5(4k) = 20k

This also means that our composite function changes value depending on the value of k.

Conclusion: g(k) becomes input for function f.

(8 votes)

awesomeness.RM

8 years agoPosted 8 years ago. Direct link to awesomeness.RM's post “Can someone please simpli...”

Can someone please simplify all of this for me cause i am so confused!

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(2 votes)

Kim Seidel

8 years agoPosted 8 years ago. Direct link to Kim Seidel's post “Sometimes it's useful to ...”

Sometimes it's useful to look at a different point of view. Try this site. Then come back and try this video again. http://www.mathsisfun.com/sets/functions-composition.html

(6 votes)

Mercado Oscar

10 months agoPosted 10 months ago. Direct link to Mercado Oscar's post “Number 3 is hard can u gi...”

Number 3 is hard can u give better explanations

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(4 votes)

jakubjwerner

10 months agoPosted 10 months ago. Direct link to jakubjwerner's post “The way I understand it a...”

The way I understand it and I solve it is to always split solution in to steps where each step is solving just single function:

f(x) = 3x-5

g(x) = 3-2x

(g∘f)(3)1. We'll solve f(x) as it's on the end. We know that x is 3 so we need to calculate 3*3-5 which is 4

2. We'll solve g(x). g(x) is wrapping up f(x) so it might look something like g(f(x)) = 3-2(fx) = 3-2(3x-5).

As we know from step 1 that f(x) = 4 we can just use it as x variable for g. So equation should be g(x) = 3-2*4

Esentially you can just focus on single function and use your result as x of next function.

I hope this is helpful and not more confusing.

(2 votes)

Jennifer Laessig

7 years agoPosted 7 years ago. Direct link to Jennifer Laessig's post “If f(x)=(1/x) and (f/g)(x...”

If f(x)=(1/x) and (f/g)(x)=((x+4)/(x^2+2x)), what is the function g?

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(4 votes)

Kim Seidel

7 years agoPosted 7 years ago. Direct link to Kim Seidel's post “Based upon the rules for ...”

Based upon the rules for dividing with fractions: f/g = (1/x) / g = (1/x) * the reciprocal of g

We need to work in reverse

1) Factor denominator to undo the multiplication:`(x+4)/(x^2+2x)`

=`(x+4)/[x(x+2)]`

We can see there is a factor of X in the denominator. This would have been from multiplying 1/x * the reciprocal of g.

2) Separate the factor 1/x:`(1/x) * (x+4)/(x+2)`

This tells us the reciprocal of g =`(x+4)/(x+2)`

3) Flip it to find g:

`g(x) = (x+2)/(x+4)`

Hope this helps.

(2 votes)