Math Problem Statement

Analyze the function f(x) = 1 + cos(x), including properties such as domain, range, and behavior.

Solution

The image shows a mathematical function notation, which appears to be:

f(x)=1+cos(x)f(x) = 1 + \cos(x)

It seems like there might also be a question related to finding the range, domain, or some other property of this function, though it's not fully visible.

Would you like help analyzing specific properties of f(x)=1+cos(x)f(x) = 1 + \cos(x), such as finding the range, domain, or calculating derivatives?


Here are five related questions that build on this function:

  1. What is the domain of the function f(x)=1+cos(x)f(x) = 1 + \cos(x)?
  2. What is the range of f(x)=1+cos(x)f(x) = 1 + \cos(x)?
  3. How does f(x)=1+cos(x)f(x) = 1 + \cos(x) behave as xx approaches positive and negative infinity?
  4. What is the derivative of f(x)=1+cos(x)f(x) = 1 + \cos(x) with respect to xx?
  5. How would you sketch the graph of f(x)=1+cos(x)f(x) = 1 + \cos(x)?

Tip: Remember that the range of a cosine function, shifted or scaled, depends on its amplitude and any vertical shifts applied.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Functions
Cosine Function

Formulas

f(x) = 1 + cos(x)
Domain of cosine function: (-∞, ∞)
Range of cosine function: [-1, 1]

Theorems

Properties of trigonometric functions

Suitable Grade Level

Grades 9-12