In Exercises 55–58, find the indicated function values for each function. ____ g(x) = −³√8x−8; g(2), g(1), g(0)

Key Concepts

Cube Root Function

The cube root function, denoted as ∛x, is the inverse of the cubic function. It takes a number and returns the value that, when cubed, gives the original number. For example, ∛8 = 2 because 2³ = 8. Understanding this function is crucial for evaluating g(x) = −³√(8x−8) as it involves calculating the cube root of an expression.

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For instance, to find g(2), you replace x in g(x) with 2, resulting in g(2) = −³√(8(2)−8). This process is essential for finding the indicated function values in the problem.

Algebraic Manipulation

Algebraic manipulation refers to the techniques used to simplify or rearrange expressions and equations. In the context of the given function g(x), it involves simplifying the expression inside the cube root before evaluating it. Mastery of these skills is necessary to accurately compute the function values g(2), g(1), and g(0).