# Proving Equivalence of f(x) and g(x)

• MHB
• pappoelarry
In summary, the conversation discusses two functions f(x) and g(x) and their equivalence. It is asked to multiply out f(x) and provide the steps and answer. The response suggests taking an Algebra course as the first step to solving the problem.
pappoelarry
Consider the two functions f(x)=(x-1)(x4+x³+x²+x+1) and g(x)=x5-1. If they are equivalent, prove they are; if they are not equivalent, prove they aren't.

Multiply out f(x). What do you get?

-Dan

topsquark said:
Multiply out f(x). What do you get?

-Dan
huh
post the steps and ans. plss

Can you multiply out polynomials? $$\displaystyle (x - 1)(x^2 + x + 1) = x(x^2 + x + 1) - (x^2 + x + 1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1$$ for example.

-Dan

pappoelarry said:
huh
post the steps and ans. plss
Step one: take an Algebra Course!

(Where did you get this problem?)

pappoelarry said:
huh
post the steps and ans. plss
First step- take an eighth or nineth grade (13 or 14 year old) algebra class!

## 1. How do you prove equivalence of two functions?

To prove equivalence of two functions, you must show that they have the same output for every possible input. This can be done by using algebraic manipulation, substitution, or graphing the functions to show that they have the same shape and behavior.

## 2. What is the purpose of proving equivalence of functions?

The purpose of proving equivalence of functions is to show that they are essentially the same function, just written in different forms. This can help simplify complex expressions and make it easier to understand and solve problems involving the functions.

## 3. Can two functions be equivalent but not identical?

Yes, two functions can be equivalent but not identical. This means that they have the same output for every input, but they may be written in different forms. For example, f(x) = x^2 and g(x) = (x+1)^2 are equivalent but not identical.

## 4. What are some common techniques for proving equivalence of functions?

Some common techniques for proving equivalence of functions include algebraic manipulation, substitution, and graphing. Other techniques may include using properties of functions, such as the commutative or distributive property.

## 5. Can you prove equivalence of functions without using algebra?

Yes, equivalence of functions can be proven without using algebra. This can be done by graphing the functions and showing that they have the same shape and behavior, or by using other techniques such as substitution or properties of functions.

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