Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

If [tex]\( f(x) = x^3 \)[/tex], then [tex]\( f^{-1}(x) = \)[/tex] [tex]\(\square\)[/tex].

Sagot :

To find the inverse function of [tex]\( f(x) = x^3 \)[/tex], we follow these steps:

1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = x^3 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse:
[tex]\[ x = y^3 \][/tex]

3. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = x^{1/3} \][/tex]

4. Since we denote the inverse function as [tex]\( f^{-1}(x) \)[/tex], we have:
[tex]\[ f^{-1}(x) = -1 \][/tex]

So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is [tex]\(\boxed{-1}\)[/tex].