**Question 29**Let \( f: \mathbb{R} \to \mathbb{R} \) where \( f(x) = x^2 + 2 \). Which of the following is \( f^{-1}((2,11)) \)?- \( (-3, 0) \)- \( (0, 3) \)- \( (-3, 3) \)- \( (-3, 3) - \{0\} \) (Selected)**Explanation:**The function \( f(x) = x^2 + 2 \) is a quadratic function. The inverse \( f^{-1} \) for the interval \((2, 11)\) is determined by finding the values of \( x \) such that the range from 2 to 11 is covered. For \( f(x) = x^2 + 2 \), we have:- \( f(x) = 2 \) when \( x^2 = 0 \), so \( x = 0 \).- \( f(x) = 11 \) when \( x^2 = 9 \), so \( x = \pm 3 \).Thus, \( f^{-1}((2, 11)) \) corresponds to the \( x \)-values in the interval \((-3, 3)\) excluding \( x = 0\).

Consider the given function, fx=x2+2fx-2=x2x=±fx-2

Answered: Let f: R→R where f(x)=x²+2.Which of the…

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Let f: R→R where f(x)=x²+2.Which of the following is f((2,11))? O (-3,0) O (0,3) O (-3,3) (-3,3)-{0}

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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