# Solving for x: Are F(x) and G(x) Equivalent?

• brycenrg
In summary, the conversation is discussing the functions F(x) = (x^2 - x)/(x-1) and G(x) = x and whether they are equal. The conversation brings up the issue of dividing by zero and manipulating equations, as well as the importance of specifying the domain of a function. Ultimately, it is impossible to determine if F(x) and G(x) are equal without knowing their specified domains.
brycenrg
F(x) = (x^2 - x)/(x-1)
G(x)= x

I factored x^2-x and canceled denominator of f(x) which simplify to x

So it does equal x does not now matter that in original equation x cannot = 1 otherwise denominator = 0

I'm just making sure they are = and but maybe not equivalent. Trying to learn more of maths. Thank you.

Is F(x) defined when x=1? Is G(x) defined there?

ehild

The problem doesn't say

Can you divide by zero? ehild

No but you can manipulate the equation to be x.

You manipulated it by dividing with an expression that can be zero. It is forbidden.
Try to input (1^2-1)/(1-1) in your calculator . What does it say?

ehild

Do F and G have the same domains?

brycenrg said:
The problem doesn't say

If it doesn't state the domains then, strictly speaking, it is impossible to say whether the functions are equal. I can claim the functions f = x and g = 2x are equal if the domain is {0}. Conversely, f = x and g = x are different functions if I specify different domains.

If no value is specified for F(1), is 1 in F's domain?
Consider whether 1 might be in G's domain, and the consequences.

brycenrg said:
The problem doesn't say
It might be that the domains are implied - that is, the domain for each function might be the real numbers for which each function is defined. It might be that this is actually stated in the problem and you didn't include it in the problem description.

If there actually isn't any information given in the problem, what would be the implied domains for F and G?

## 1. What is the difference between F(x) and G(x)?

F(x) and G(x) are both mathematical functions that involve an input variable, x, and produce an output based on the function's definition. The main difference between the two is that F(x) and G(x) may have different mathematical expressions or algorithms to determine their output values.

## 2. How do you solve for x in F(x) and G(x) equations?

To solve for x in F(x) and G(x) equations, you need to isolate the variable x on one side of the equation by using algebraic operations such as addition, subtraction, multiplication, and division. This will help you find the value of x that satisfies both equations simultaneously.

## 3. Can F(x) and G(x) be equivalent without having the same values for x?

Yes, it is possible for F(x) and G(x) to be equivalent without having the same values for x. This is because the two functions can have different expressions or algorithms, but still produce the same output values for a given input. In other words, the functions may have different x values, but they will result in the same y value.

## 4. How do you check if F(x) and G(x) are equivalent?

To check if F(x) and G(x) are equivalent, you can plug in the same value for x in both equations and compare the resulting output values. If they are the same, then the functions are equivalent. Another way to check is by graphing both functions and seeing if they produce the same line or curve.

## 5. What is the importance of solving for x in F(x) and G(x) equations?

Solving for x in F(x) and G(x) equations is important because it allows us to find the values of x that make both equations true. This can help us understand the relationship between the two functions and how they behave for different input values. It also allows us to solve real-world problems that involve finding an unknown variable in a mathematical equation.

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