Use the table to evaluate the given compositions. <IMAGE>


g(h(ƒ(4)))

Verified step by step guidance

1. Identify the innermost function in the composition, which is \( f(4) \).
2. Use the table to find the value of \( f(4) \).
3. Substitute the value of \( f(4) \) into the next function, \( h(f(4)) \).
4. Use the table to find the value of \( h(f(4)) \).
5. Substitute the value of \( h(f(4)) \) into the outermost function, \( g(h(f(4))) \), and use the table to find the final value.

Key Concepts

Function Composition

Function composition involves combining two or more functions to create a new function. If you have functions f, g, and h, the composition g(h(f(x))) means you first apply f to x, then apply h to the result of f, and finally apply g to the result of h. Understanding how to evaluate compositions is crucial for solving problems that involve multiple functions.

Evaluating Functions

Evaluating functions requires substituting a specific input value into the function's formula. For example, if f(x) = x + 2, then f(4) = 4 + 2 = 6. This process is essential for function composition, as each function's output becomes the input for the next function in the composition.

Order of Operations

The order of operations dictates the sequence in which mathematical operations should be performed to ensure accurate results. In function composition, this means evaluating from the innermost function to the outermost. This principle is vital when dealing with nested functions, as it affects the final outcome of the composition.