By now, you should have seen my first post on functions. This section's concept is relatively simple and easy to understand. To put it simply, function composition is when one function is put into another function.
Function composition often takes its form like this: f(g(x)). In this form, it is basically saying that with an "x" input into the function of "g," the output for that function becomes the input for the function "f."
Function composition problems usually come with two different or even identical functions. Then it will tell you what the "x" value is, and you substitute that "x" value in for the function that is written out.
ex.
f(x) = 1/3x + 5
g(x) = 3x - 4
You are given two functions in this example, and the question might be something along the lines of: f(g(3))
Start out first with the g(3) part. Substitute 3 in for all x's in the function.
g(3) = 3(3) - 4
g(3) = 9 - 4
g(3) = 5
Now you have an output for the function g(x). This output becomes the input for the function of f(x).
f(5) = 1/3(5) + 5
f(5) = 5/3 + 5
f(5) = 1 2/3 + 5
f(5) = 6 2/3 or f(5) = 20/3
On occasion, you might come across a question asking for f(f(x)). This may seem confusing at first, but it follows the exact same rules as the scenario explained above.
ALTERNATIVE METHOD
An alternative method to solving function composition problems is simply plugging in the entire equation into the other.
ex.
f(x) = 10x - 3
g(x) = 3x - 4
find f(g(x))
A different approace to this problem is to simply plug the entire function into the other. f(g(x)) is stating that with the function g(x) as the "x" value for function f(x), f(g(x)) is the output.
f(g(x))
f(3x - 4) = 10(3x - 4) - 3
f(3x - 4) = 30x - 40 - 3
f(3x - 4) = 30x - 43
After this, you may plug in any value for "x" as the question requests and you will receive the same answer as the previous method.
Good luck! Let me know if you would like me to answer any questions about this concept or if I could clarify on something for you, drop a comment! :)
Sunday, September 19, 2010
Monday, September 13, 2010
Math Concept: Functions
Functions are defined as a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
(definition by wordnetweb.princeton.edu/perl/webwn)
In other words, for every "y" value, there is a unique "x" value, such that a "x" value does NOT have more than ONE "y" value. This is one of the key defining factors of a function, and can be tested by a method commonly referred to as the vertical line test.
The vertical line test is conducted by drawing a straight line that forms a 90 degree angle with the x-axis through any point on the graph. If the relationship is truly a function, then it will pass the vertical line test at any location on its graph, modeling the relationship in which there is a unique "x" for every "y."
Functions are used to find the out put of an equation when a certain input is plugged in. They are often written in the form - f(x) - in which the entire expression - f(x) - is the "y" value, and the - (x) - is the "x" input.
To find the output, the function will give you an "x" value to plug in by writing it like this: f(3) in which "3" is the "x" value you are substituting
The written form of a function basically says, if THIS value is plugged in for EVERY "x" in the equation, then THAT value will come out.
ex. f(x) = 10x + 5
f(4) = 10(4) + 5
f(4) = 40 + 5
f(4) = 45
This states that for THIS function, and input of "4" as the "x" value gives you an output of "45" as the "y" value. this point on a coordinate place would be plotted as (4, 45).
This will be my first actual concept post on this blog. This is simply a test to see what method I should use in order to tutor people more efficiently. If you have any requests for this post or would like me to make a post on another concept, be sure to drop me a comment and I'll get to work on it as soon as I can, good luck! :)
(definition by wordnetweb.princeton.edu/perl/webwn)
In other words, for every "y" value, there is a unique "x" value, such that a "x" value does NOT have more than ONE "y" value. This is one of the key defining factors of a function, and can be tested by a method commonly referred to as the vertical line test.
The vertical line test is conducted by drawing a straight line that forms a 90 degree angle with the x-axis through any point on the graph. If the relationship is truly a function, then it will pass the vertical line test at any location on its graph, modeling the relationship in which there is a unique "x" for every "y."
Functions are used to find the out put of an equation when a certain input is plugged in. They are often written in the form - f(x) - in which the entire expression - f(x) - is the "y" value, and the - (x) - is the "x" input.
To find the output, the function will give you an "x" value to plug in by writing it like this: f(3) in which "3" is the "x" value you are substituting
The written form of a function basically says, if THIS value is plugged in for EVERY "x" in the equation, then THAT value will come out.
ex. f(x) = 10x + 5
f(4) = 10(4) + 5
f(4) = 40 + 5
f(4) = 45
This states that for THIS function, and input of "4" as the "x" value gives you an output of "45" as the "y" value. this point on a coordinate place would be plotted as (4, 45).
This will be my first actual concept post on this blog. This is simply a test to see what method I should use in order to tutor people more efficiently. If you have any requests for this post or would like me to make a post on another concept, be sure to drop me a comment and I'll get to work on it as soon as I can, good luck! :)
Sunday, September 12, 2010
Math Concepts Tutoring start
Hey guys! Atharva Dhole here. This is my first post on my Math concepts tutoring blog, and there will definitely be many many more. I have started this blog to help anyone with any math concepts that they require help on. Note: I'm only 15 and I may not even have began many of the math concepts that you require help in, so i apologize ahead for any inconvenience.
I may know what you require help in, so if i do, then please let me know and i'll make posts on that concept that can help you gain a better understanding of the concept. I believe that understanding the concept behind something, whether it be in math or reading or any subject, is much more important than being able to simply solve the problems put in front of you.
I encourage regular visits to this blog and let me know if you have any reccomendations for new concepts! Thank you everyone and i hope i can be of as much as help as possible!
Good luck! Please follow my blog! :)
-Atharva Dhole
I may know what you require help in, so if i do, then please let me know and i'll make posts on that concept that can help you gain a better understanding of the concept. I believe that understanding the concept behind something, whether it be in math or reading or any subject, is much more important than being able to simply solve the problems put in front of you.
I encourage regular visits to this blog and let me know if you have any reccomendations for new concepts! Thank you everyone and i hope i can be of as much as help as possible!
Good luck! Please follow my blog! :)
-Atharva Dhole
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