Final answer:
The function presented is a polynomial, and its 'power' relates to the exponents of its variables. Raising expressions to a power affects each term, and inverse operations, such as taking a root, may be used to 'undo' a power. The power rule is applied when differentiating terms from powers.
Step-by-step explanation:
The function given is f(x) = 2x^3 - 3x^2 + 7. In mathematics, when dealing with functions and especially polynomials, the term power refers to the exponent applied to a variable. For instance, in the term 2x^3, the number 3 is the power of the variable x, indicating that x should be multiplied by itself twice (since x to the first power is just x). When raising expressions inside parentheses to a power, it is important to remember that the power applies to every term inside those parentheses. Additionally, for solving equations that cannot be easily factored or simplified, we might utilize the quadratic formula or other methods depending on the structure of the equation. When we need to 'undo' a power, such as finding the side length of a triangle given the hypotenuse using the Pythagorean theorem, we often take the square root, which is the inverse operation of squaring. Similarly, when differentiating a function involving powers, we decrease the power by one and multiply it by the original power, according to the power rule of differentiation.