Let's solve the problems from the image you uploaded.

Problem 1:

You are asked to find the inverse of the function $f(x) = 3x - 4$.

Steps to find the inverse:

1. Start with $f(x) = y = 3x - 4$.
2. Solve for $x$ in terms of $y$: $y = 3x - 4 \implies x = \frac{y + 4}{3}$
3. Replace $y$ with $x$ to express the inverse: $f^{-1}(x) = \frac{x + 4}{3}$

Thus, the inverse of the function is $f^{-1}(x) = \frac{x + 4}{3}$.

Problem 2:

You are given $f(x) = 2x + 3$, and you're asked to find $f^{-1}(x)$.

Steps to find the inverse:

1. Start with $f(x) = y = 2x + 3$.
2. Solve for $x$ in terms of $y$: $y = 2x + 3 \implies x = \frac{y - 3}{2}$
3. Replace $y$ with $x$: $f^{-1}(x) = \frac{x - 3}{2}$

Thus, the inverse of the function is $f^{-1}(x) = \frac{x - 3}{2}$, which corresponds to the third option in Question 2.

Would you like further clarification or details on these steps?

Follow-up Questions:

1. How would you find the inverse of a quadratic function?
2. What does it mean for a function to be "one-to-one"?
3. Can all functions have an inverse? Why or why not?
4. How do you graphically interpret the inverse of a function?
5. What are the conditions under which a function's inverse is also a function?

Tip: Always check that the inverse function, when composed with the original function, returns the identity $f(f^{-1}(x)) = x$.