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pappoelarry
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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.
huhtopsquark said:Multiply out f(x). What do you get?
-Dan
Step one: take an Algebra Course!pappoelarry said:huh
post the steps and ans. plss
First step- take an eighth or nineth grade (13 or 14 year old) algebra class!pappoelarry said:huh
post the steps and ans. plss
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.
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.
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.
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.
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.