Solve Linear Equation for Extra Credit: f(x+a)=f(x^2+a)

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In summary, to solve a linear equation with an extra credit term, you must isolate the variable, use properties of equality, and substitute the value back into the equation. An example would be solving f(x+a)=f(x^2+a) for x=√a, giving us f(2a). The properties of equality used include addition and multiplication. Substitution can also be used to solve for the extra credit term. It is possible to have more than one solution when solving a linear equation with an extra credit term. This would occur if the original equation has multiple variables and solving for one variable results in multiple solutions for the other variable.
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CBrent
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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. Can anyone tell me?

Edit: I posted in the wrong section... moving it now.
 
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  • #2
CBrent said:
f(x+a) = f(x^2+a)
what is x?

Depends on what f and a are... are you given the function f? Or are you asked to determine a function f such that the relation you wrote down holds true for every x? Or something completely different?
 

FAQ: Solve Linear Equation for Extra Credit: f(x+a)=f(x^2+a)

How do you solve a linear equation with an extra credit term?

To solve a linear equation with an extra credit term, you must first isolate the variable on one side of the equation. Then, you can use the properties of equality to solve for the variable. Finally, you can substitute the value of the variable back into the equation to solve for the extra credit term.

Can you provide an example of solving a linear equation with an extra credit term?

Yes, for the equation f(x+a)=f(x^2+a), we can first isolate the variable by subtracting f(x) from both sides, giving us a=x^2. Then, we can take the square root of both sides to solve for x, giving us x=√a. Finally, we can substitute this value back into the original equation to solve for the extra credit term, giving us f(√a+a)=f(a+a)=f(2a).

What are the properties of equality used in solving a linear equation with an extra credit term?

The properties of equality used in solving a linear equation with an extra credit term include the addition property of equality, which allows you to add or subtract the same number to both sides of an equation, and the multiplication property of equality, which allows you to multiply or divide both sides by the same number.

Can you use substitution to solve a linear equation with an extra credit term?

Yes, substitution can be used to solve a linear equation with an extra credit term. This involves substituting the value of the variable back into the original equation to solve for the extra credit term.

Is it possible to have more than one solution when solving a linear equation with an extra credit term?

Yes, it is possible to have more than one solution when solving a linear equation with an extra credit term. This would occur when the original equation has multiple variables, and solving for one variable results in multiple solutions for the other variable.

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