Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

To determine the inverse of the function [tex]f[/tex], follow these steps:

1. Replace [tex]f(x)[/tex] with [tex]y[/tex].
2. Switch [tex]x[/tex] and [tex]y[/tex].
3. Solve for [tex]y[/tex].

The resulting function can be written as:
[tex]\[ f^{-1}(x) = (x - )^3. \][/tex]

Note: Some elements in the provided text seem incomplete or out of place. Ensure the missing components (e.g., missing values or placeholders) are filled in accurately.


Sagot :

Sure, let's carefully determine the inverse of the given function step by step.

Given the function:
[tex]\[ f(x) = \sqrt[3]{8x + 4} \][/tex]

Step 1: Set \( f(x) \) to \( y \):
[tex]\[ y = \sqrt[3]{8x + 4} \][/tex]

Step 2: Switch \( x \) and \( y \):
[tex]\[ x = \sqrt[3]{8y + 4} \][/tex]

Step 3: Solve for \( y \):
- Cube both sides to remove the cube root:
[tex]\[ x^3 = 8y + 4 \][/tex]

- Subtract 4 from both sides to isolate the term with \( y \):
[tex]\[ x^3 - 4 = 8y \][/tex]

- Divide by 8 to solve for \( y \):
[tex]\[ y = \frac{x^3 - 4}{8} \][/tex]

The inverse function \( f^{-1}(x) \) is therefore:
[tex]\[ f^{-1}(x) = \frac{x^3 - 4}{8} \][/tex]

Now we can evaluate both \( f(0) \) and \( f^{-1}(0) \).

1. Evaluate \( f(0) \):
[tex]\[ f(0) = \sqrt[3]{8 \cdot 0 + 4} = \sqrt[3]{4} \approx 1.587 \][/tex]

2. Evaluate \( f^{-1}(0) \):
[tex]\[ f^{-1}(0) = \frac{0^3 - 4}{8} = \frac{-4}{8} = -0.5 \][/tex]

Thus, the results are [tex]\( f(0) \approx 1.587 \)[/tex] and [tex]\( f^{-1}(0) = -0.5 \)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.