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You can find the definition of the function, a statement about the function's values, and an inductive proof, in the Wikipedia article "Carmichael function", which I won't repeat here.

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8y ago

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What does the horizontal line test prove?

I posted this question myself to be honest because i wasn't sure... but the horizontal line test was made to prove whether the function/graph was an one-to-one function


How would you prove algebraically that the function f(x) x-2 x 2 is one to one?

How would you prove algebraically that the function: f(x)= |x-2|, x<= 2 , is one to one?


What mathematical operation is used to prove a function has an inverse?

To prove that a function has an inverse, one typically uses the operation of checking for injectivity (one-to-one property). This involves showing that if ( f(a) = f(b) ), then ( a = b ). If the function is injective, it ensures that each output is produced by a unique input, which is essential for the existence of an inverse function. Additionally, for functions defined on the entire real line, demonstrating that the function is also surjective (onto) can further confirm the existence of an inverse.


How can you determine when a function is increasing or decreasing?

Assuming the function is linear, the direction of the function can be determined by the coefficient's sign:[y = mx + b]Where m is the coefficient of x, if m is negative, then the function is increasing. If m is positive, the function is decreasing (this relationship is rather complicated and requires advanced calculus to prove).


How do you prove if the given function is a constant function using Mean Value Theorem?

The Mean Value Theorem states that the function must be continuous and differentiable over the whole x-interval and there must be a point in the derivative where you plug in a number and get 0 out.(f'(c)=0). If a function is constant then the derivative of that function is 0 => any number you put in, you will get 0 out. Thus, using the MVT we deduced that the slope must be zero and since the f(x) is a constant function then the slope IS 0.