Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(3)

Key Concepts

Function Composition

Function composition involves combining two functions to create a new function. The notation (g ○ ƒ)(x) means to apply function ƒ first and then apply function g to the result. In this case, you would first evaluate ƒ(3) and then use that output as the input for g.

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For ƒ(x) = √(x-2), the expression under the square root must be non-negative, meaning x must be greater than or equal to 2. Understanding the domain is crucial for determining valid inputs when composing functions.

Evaluating Functions

Evaluating a function involves substituting a specific value into the function's equation to find the corresponding output. For example, to find (g ○ ƒ)(3), you first evaluate ƒ(3) and then substitute that result into g. This process requires careful calculation and an understanding of how to manipulate algebraic expressions.