Understanding and Solving Functions: A Guide to Solving Complex Equations

  • Thread starter melvinator
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In summary, the problem asks you to solve for x in terms of y. You clear the fractions by multiplying both sides by the lowest common denominator. The rest is uncomplicated simple algebra.
  • #1
melvinator
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I am having a hard time understanding how to solve functions.I am working on the following problem

Given the equation (y-x/6) - (3x-y/9) = 4 - (x+2y/4) + (x+4y/12)

g(y) is .....?

Homework Equations





The Attempt at a Solution

 
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  • #2
Your problem description does not give any information about g(y); and does not show in any way how g(y) is related to the equation. If "x" is the variable for the x-axis and "y" is the variable for the y-axis, then g(y) is a relation and not a function. Are you hoping to find the relation x=g(y) ?

EDIT: actually, without going through the solution (likely) process, I should not say that g(y) is not a function; it may well be one but we do not know until we try to solve the equation for x.
 
  • #3
That is exactly how the problem is presented in the text.Below are the 4 answer choices I am given.Maybe they will give some clue as to what they want.

1. 0.632x+12
2. 0.750y+12
3. 1.333y-12
4. 1.333x-12
 
  • #4
The equation is linear in x and y, so the equation is of a line. Since the problem asks for g(y), I interpret this to mean that it asks you to solve for x in terms of (as a function of) y. Collect all of the terms involving x on one side, and all of the terms involving y on the other side.

After working this problem, I don't get any of the answers you show, which leads me to believe that you have not given us the problem as it appears in your book.

You wrote
(y-x/6) - (3x-y/9) = 4 - (x+2y/4) + (x+4y/12)

Most of the people in this forum interpret the expression in the first pair of parentheses as
[tex]y - \frac{x}{6}[/tex]
and similarly for the other parenthesized expressions.

Does this expression appear in your text in this way:
[tex]\frac{y - x}{6}[/tex]
?
These are not the same. If you don't know how to use LaTeX, you need to put parentheses in the right places. For example, the expression just above should be written as (y - x)/6. The same goes for all of the other expressions in parentheses.
 
  • #5
Please forgive me,this is my first post.Below is the equation in the correct format

(y-x)/6 - (3x-y)/9 = 4 - (x+2y)/4 + (x+4y)/12
 
  • #6
You are apparently looking for an expression for x. Your equation given uses rational expressions. Clear the fractions by multiplying both sides by the lowest common denominator. The rest will be uncomplicated simple algebra.
 

1. What is a function in mathematics?

A function is a mathematical relationship between two or more variables. It takes in one or more inputs, performs a specific operation on them, and produces an output. In simpler terms, a function is a rule that links an input to an output.

2. How do you solve for a function?

To solve for a function, you need to find the value of the variable that makes the function equation true. This is usually done by using algebraic techniques such as substitution, elimination, and factoring. Once you have found the value of the variable, you can plug it back into the function to get the corresponding output.

3. What are the different types of functions?

There are several types of functions in mathematics, including linear, quadratic, exponential, logarithmic, trigonometric, and polynomial functions. Each type has a unique form and properties that determine how it behaves and can be solved.

4. What is the domain and range of a function?

The domain of a function is the set of all possible input values or independent variables that the function can take. The range of a function is the set of all possible output values or dependent variables that the function can produce. Both the domain and range can be infinite or finite, depending on the function.

5. How do you graph a function?

To graph a function, you need to plot the points that satisfy the function's equation on a coordinate plane. You can use a table of values, a graphing calculator, or algebraic techniques such as finding the intercepts and slope to plot the points accurately. Once the points are plotted, you can connect them with a smooth curve to get the graph of the function.

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