Questions: Quiz U5S2 Quiz dentonisd. instructure.com/courses/279466/quizzes/517308/take Question 2 Given f(x)=1/3(x+2)^3-1, find the inverse function. - A. f^(-1)(x)=3√(3(x-1))-2 - B. f^(-1)(x)=3√(3(x+1))-2 - C. f^(-1)(x)=3√(3(x+2))-1 - D. f^(-1)(x)=3 3√(x+1)-2 A B C D

Quiz U5S2 Quiz
dentonisd. instructure.com/courses/279466/quizzes/517308/take

Question 2

Given f(x)=1/3(x+2)^3-1, find the inverse function.
- A. f^(-1)(x)=3√(3(x-1))-2
- B. f^(-1)(x)=3√(3(x+1))-2
- C. f^(-1)(x)=3√(3(x+2))-1
- D. f^(-1)(x)=3 3√(x+1)-2
A
B
C
D

Transcript text: Quiz U5S2 Quiz dentonisd. instructure.com/courses/279466/quizzes/517308/take Question 2 Given $f(x)=\frac{1}{3}(x+2)^{3}-1$, find the inverse function. - A. $f^{-1}(x)=\sqrt[3]{3(x-1)}-2$ - B. $f^{-1}(x)=\sqrt[3]{3(x+1)}-2$ - C. $f^{-1}(x)=\sqrt[3]{3(x+2)}-1$ - D. $f^{-1}(x)=3 \sqrt[3]{x+1}-2$ A B C D Question 3

Solution

Solution Steps

Step 1: Finding the Inverse Function

Given the function $ f(x) = \frac{1}{3}(x+2)^{3} - 1 $, we need to find its inverse function $ f^{-1}(x) $.

Step 2: Calculating the Inverse

Upon calculating the inverse function, we obtained: \[ f^{-1}(x) = \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 y + 3} - 2 \] This expression includes complex numbers, indicating that the function does not have a real-valued inverse for all $ x $.

Step 3: Comparing with Given Options

The calculated inverse function does not match any of the provided options:

A. $ f^{-1}(x) = \sqrt[3]{3(x-1)} - 2 $
B. $ f^{-1}(x) = \sqrt[3]{3(x+1)} - 2 $
C. $ f^{-1}(x) = \sqrt[3]{3(x+2)} - 1 $
D. $ f^{-1}(x) = 3 \sqrt[3]{x+1} - 2 $

Final Answer

Since the calculated inverse function does not correspond to any of the options provided, we conclude that none of the options are correct. Thus, the answer is: \[ \boxed{\text{None of the options are correct}} \]

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