PIL import Image

Load the image to analyze its contents

image_path = '/mnt/data/1732723792433feo4iemq.jpg' image = Image.open(image_path) image.show()I have displayed the image. Let me now process its contents to extract any relevant mathematical information. I'll provide a detailed explanation pytesseract

Use pytesseract to extract text from the image

extracted_text = pytesseract.image_to_string(image)

extracted_textThe text extracted from the image contains a mathematical problem involving functions $f$ and $g$. Here's the relevant content broken down:

1. Functions Definition:

   • $f(x) = 3x + 4$, for $x \in \mathbb{R}$
   • $g(x)$ is defined as $g(x) = \frac{1}{3}x + 8$

2. Task (i): Evaluate $f(g(2))$.

3. Task (ii): Sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, and explain the relationship between the two graphs.

4. Task (iii): Obtain an expression for $g(x)$ and explain why it has an inverse.

5. Task (iv): Express both $f^{-1}(x)$ and $g^{-1}(x)$ in terms of $x$.

Would you like me to walk through these problems step by step or focus on any particular part? Feel free to ask for further details on any of these questions!

Here are some related questions you might find useful:

1. How do you evaluate the composition of functions like $f(g(2))$?
2. What is the method for finding the inverse of a linear function?
3. How do you graph a function and its inverse?
4. What are the properties of functions that have an inverse?
5. How do you determine if two functions are inverses of each other?

Tip: When evaluating a composition of functions, always begin by evaluating the inner function first, and then apply the outer function to