Solve Linear Equation f(x+a)=f(x^2+a) - Help Needed

  • Thread starter CBrent
  • Start date
In summary, the conversation is about a student seeking help with a linear equation for extra credit. They are unsure how to approach the problem and are looking for guidance on how to find the value of x. The conversation also touches on the concept of linear functions being invertible.
  • #1
CBrent
2
0
We are studying linear equations in school and the prof gave us this to solve for extra credit:

f(x+a) = f(x^2+a)
what is x?

I don't know what type of equation that is, so I can't even start a solution. Can anyone help guide me in the right direction?
 
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  • #2
Well, what number do you have to plug into x to get:
[tex]x=x^2[/tex]?
Because, since both are the same functions, then the numbers being inserted, assuming it is a linear function, must be the same, so:
[tex]x+a=x^2+a[/tex]
 
  • #3
CBREnt:
Did your professor say that linear function are..invertible?
 

1. What is a linear equation?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The highest power of the variable in a linear equation is 1.

2. How do I solve a linear equation?

To solve a linear equation, you need to isolate the variable on one side of the equation by using inverse operations. This means that you should perform the opposite operation on both sides of the equation in order to cancel out any terms that do not contain the variable. Once the variable is isolated, you can solve for its value.

3. What is the difference between f(x) and f(x+a)?

f(x) represents a function with a variable x, while f(x+a) represents the same function with a different input, x+a. This means that the function is being evaluated at a different point on the x-axis.

4. What does it mean to solve an equation?

Solving an equation means finding the value of the variable that makes the equation true. This is often referred to as finding the solution or the root of the equation.

5. Can you explain the process for solving "f(x+a)=f(x^2+a)"?

To solve this equation, you need to follow the steps for solving a linear equation. First, you should expand the equation using the distributive property. Then, isolate the variable on one side of the equation by performing inverse operations. Once the variable is isolated, you can solve for its value by applying the appropriate algebraic techniques. In this case, the solution will be in terms of a.

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