Composite Function
- Thread starter suicoted
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To work from these pictures, you take the x-value, go to that point on the x-axis, go up or down to find the point, and go sideways to find the y-value.
In this case, the y-value is also the f(x)-value; f(x) = y.
As pka points out, for x = 2, f(x) = 4. This is because, when you go to x = 2 and look up, the point is at y = 4.
But you're not just finding f(2). You're finding (or trying to find) f(f(2)). So you're going to take your y-value of 4 and start over again, using this as your x-value.
Trace over on the x-axis to x = 4. Where is the point that corresponds to this?
Eliz.
In this case, the y-value is also the f(x)-value; f(x) = y.
As pka points out, for x = 2, f(x) = 4. This is because, when you go to x = 2 and look up, the point is at y = 4.
But you're not just finding f(2). You're finding (or trying to find) f(f(2)). So you're going to take your y-value of 4 and start over again, using this as your x-value.
Trace over on the x-axis to x = 4. Where is the point that corresponds to this?
Eliz.
mmm4444bot
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It is not zero.
Hello suicoted:
No, x is not zero.
Think of a function as a machine. You input a value into the function. The function applies its definition to the input, and outputs the corresponding value. (In this problem, the definition of f(x) is given by a graph.)
f(2) = 4
Here, the input is 2, and the output is 4.
f(f(x)) = 4
In this composite function, the output of f(x) is being used as another input. What does f(x) need to be so that if it is input back into the function, the output will be 4?
You said that you know f(2) = 4.
Now ask yourself: What does the input need to be so that the output is 2?
In other words, find x so that f(x) = 2. Then, inputing that 2 back into the function will lead to the output of 4.
Let us know if you still don't understand the question.
~ Mark
Hello suicoted:
No, x is not zero.
Think of a function as a machine. You input a value into the function. The function applies its definition to the input, and outputs the corresponding value. (In this problem, the definition of f(x) is given by a graph.)
f(2) = 4
Here, the input is 2, and the output is 4.
f(f(x)) = 4
In this composite function, the output of f(x) is being used as another input. What does f(x) need to be so that if it is input back into the function, the output will be 4?
You said that you know f(2) = 4.
Now ask yourself: What does the input need to be so that the output is 2?
In other words, find x so that f(x) = 2. Then, inputing that 2 back into the function will lead to the output of 4.
Let us know if you still don't understand the question.
~ Mark
I'm confused too.
f(2)=4
That shows up on the graph.
Now you want to find how many f(?)=2 so you can do f(f(?))=4
Just draw a line at y=2 and count how many times it hits a line on the graph. Each intersection is an answer for the ?.
I can't see the picture well enough to tell if f(0) = 4. It depends on what kind of dot is at (0,4). You might have to draw another line at y=0 and count some more. (I doubt it though.)
f(2)=4
That shows up on the graph.
Now you want to find how many f(?)=2 so you can do f(f(?))=4
Just draw a line at y=2 and count how many times it hits a line on the graph. Each intersection is an answer for the ?.
I can't see the picture well enough to tell if f(0) = 4. It depends on what kind of dot is at (0,4). You might have to draw another line at y=0 and count some more. (I doubt it though.)