Math Problem Statement

Let f be the piecewise function given by f(x) = {8 - x^2 if x < 5, x + 8 if x ≥ 5}. Let g be an unknown function with domain (-∞, ∞). Which of the following is equal to the one-sided limit lim[x→5] g(f(x))? (Hint: Graph the function f)

Solution

Let's carefully analyze this problem step by step.

Given Information:

We have two functions:

  1. f(x)f(x) is a piecewise function defined as: [ f(x) = \begin{cases} 8 - x^2 & \text{if } x < 5, \ x + 8 & \text{if } x \geq 5. \end{

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Math Problem Analysis

Mathematical Concepts

Limits
Piecewise Functions
Continuity

Formulas

Limit of a function: lim[x→a] f(x)

Theorems

One-sided limit

Suitable Grade Level

Grades 10-12