Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Select the correct answer.

What is the inverse of this function?

[tex] f(x)=\sqrt[3]{x+12} [/tex]

A. [tex] f^{-1}(x)=x+12 [/tex]

B. [tex] f^{-1}(x)=x-12 [/tex]

C. [tex] f^{-1}(x)=12-x^3 [/tex]

D. [tex] f^{-1}(x)=x^3-12 [/tex]

Sagot :

GinnyAnswer
To find the inverse of the function \( f(x) = \sqrt[3]{x + 12} \), we need to follow these steps:

1. Rewrite the function as an equation with \( y \) and \( x \):
Let \( y = f(x) \). So, we have:
[tex]\[ y = \sqrt[3]{x + 12} \][/tex]

2. Switch the variables \( x \) and \( y \), reflecting the fact that we want the input and output exchanged:
[tex]\[ x = \sqrt[3]{y + 12} \][/tex]

3. Eliminate the cube root by cubing both sides of the equation:
[tex]\[ x^3 = y + 12 \][/tex]

4. Solve for \( y \) to isolate it:
Subtract 12 from both sides:
[tex]\[ y = x^3 - 12 \][/tex]

So, the inverse function is:
[tex]\[ f^{-1}(x) = x^3 - 12 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.