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?

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.