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Is the function f(x) = x^3 invertible?

a) Yes, it's invertible.
b) No, it's not invertible.
c) I need more information to determine invertibility.
d) It's invertible for some values of x but not for others.

User Konvas
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1 Answer

3 votes

Final answer:

The function f(x) = x^3 is invertible because it is a one-to-one function and for every value of f(x), there is a unique x, making it both injective and surjective.

Step-by-step explanation:

The function f(x) = x^3 is invertible because it is a one-to-one function. In mathematical terms, a function is invertible if and only if it is bijective, which means it is both injective (one-to-one) and surjective (onto). A cubic function like f(x) = x^3 is one-to-one because each value of x produces a unique value of f(x), and it is onto because for every possible value of f(x), there exists a corresponding value of x. To find the inverse of the cubic function, we would solve for x in terms of y, where y = x^3. This involves taking the cubic root of both sides of the equation: x = √y. Therefore, the correct answer is (a) Yes, it's invertible.

User Kanak Sony
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