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What is the domain for the exponential function f(x) = -5log(x-2)? OD: (xe R) OD: (xe R|x>-2) OD: (XERIX > 2) OD: (XER|x>3)

What is the domain for the exponential function f(x) = -5log(x-2)? OD: (xe R) OD: (xe R|x>-2) OD: (XERIX > 2) OD: (XER|x>3)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question:** What is the domain for the exponential function \( f(x) = -5 \log(x - 2) \)? **Answer Choices:** - ⃝ \( D: \{ x \in ℝ \} \) - ⃝ \( D: \{ x \in ℝ | x > -2 \} \) - ⃝ \( D: \{ x \in ℝ | x > 2 \} \) - ⃝ \( D: \{ x \in ℝ | x > 3 \} \) **Explanation:** In the given question, you are asked to determine the domain of the exponential function \( f(x) = -5 \log(x - 2) \). The function involves a logarithm, \(\log(x - 2)\), and the argument of a logarithm function should be positive. Therefore, the expression inside the logarithm must be greater than zero. Hence, solve the inequality: \[ x - 2 > 0 \] \[ x > 2 \] Therefore, the domain of the function \( f(x) \) is all real numbers greater than 2. Thus, the correct answer is: ⃝ \( D: \{ x \in ℝ | x > 2 \} \)
Transcribed Image Text:**Question:** What is the domain for the exponential function \( f(x) = -5 \log(x - 2) \)? **Answer Choices:** - ⃝ \( D: \{ x \in ℝ \} \) - ⃝ \( D: \{ x \in ℝ | x > -2 \} \) - ⃝ \( D: \{ x \in ℝ | x > 2 \} \) - ⃝ \( D: \{ x \in ℝ | x > 3 \} \) **Explanation:** In the given question, you are asked to determine the domain of the exponential function \( f(x) = -5 \log(x - 2) \). The function involves a logarithm, \(\log(x - 2)\), and the argument of a logarithm function should be positive. Therefore, the expression inside the logarithm must be greater than zero. Hence, solve the inequality: \[ x - 2 > 0 \] \[ x > 2 \] Therefore, the domain of the function \( f(x) \) is all real numbers greater than 2. Thus, the correct answer is: ⃝ \( D: \{ x \in ℝ | x > 2 \} \)
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