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The image describes a mathematical function \( f(x) = 5x - 7 \) and asks how many of the following statements are true, based on the information provided:

1. \( f^{-1}(-2) = 1 \)
2. \( f^{-1}(0) = 2 \)
3. \( f^{-1}(3) = 3 \)
4. \( f^{-1}(7) = 4 \)

We are dealing with the inverse function \( f^{-1}(x) \), which means we need to solve for \( x \) in the equation \( f(x) = y \), where \( y \) is given.

### Step 1: Determine the inverse function \( f^{-1}(x) \)
We start with the function \( f(x) = 5x - 7 \). To find the inverse, follow these steps:

1. Set \( y = f(x) = 5x - 7 \).
2. Solve for \( x \) in terms of \( y \):

\[
y = 5x - 7
\]
\[
y + 7 = 5x
\]
\[
x = \frac{y + 7}{5}
\]

So, the inverse function is:

\[
f^{-1}(x) = \frac{x + 7}{5}
\]

### Step 2: Evaluate the statements

1. \( f^{-1}(-2) = 1 \)
   \[
   f^{-1}(-2) = \frac{-2 + 7}{5} = \frac{5}{5} = 1
   \]
   This is **true**.

2. \( f^{-1}(0) = 2 \)
   \[
   f^{-1}(0) = \frac{0 + 7}{5} = \frac{7}{5} = 1.4
   \]
   This is **false**.

3. \( f^{-1}(3) = 3 \)
   \[
   f^{-1}(3) = \frac{3 + 7}{5} = \frac{10}{5} = 2
   \]
   This is **false**.

4. \( f^{-1}(7) = 4 \)
   \[
   f^{-1}(7) = \frac{7 + 7}{5} = \frac{14}{5} = 2.8
   \]
   This is **false**.

### Conclusion:
Only the first statement is true. Therefore, the correct answer is **1**.

Would you like any further details or clarifications?

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Here are 5 related questions:
1. How do you calculate the inverse of a quadratic function?
2. What are the conditions for a function to have an inverse?
3. Can every linear function have an inverse? Why or why not?
4. How would the graph of \( f(x) = 5x - 7 \) and its inverse look?
5. How does the process of finding the inverse change for non-linear functions?

**Tip:** Always verify if a function is one-to-one before attempting to find its inverse.

The image describes a mathematical function f(x) = 5x - 7 and asks how many of the following statements are true: (1) f^{-1}(-2) = 1, (2) f^{-1}(0) = 2, (3) f^{-1}(3) = 3, (4) f^{-1}(7) = 4.

This problem involves finding the inverse of the linear function f(x) = 5x - 7 and evaluating specific statements. Learn how to calculate the inverse and verify if the provided statements are true. Suitable for students in Grades 9-11.

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