Final answer:
The inverse function of f(x) = 4x + 7 is f^{-1}(x) = (x - 7) / 4.
Step-by-step explanation:
The question asks us to find the inverse function, often denoted as f^{-1}(x), for the given function f(x) = 4x + 7. To find the inverse function, we follow a series of steps: first, we replace f(x) with y, making the equation y = 4x + 7. Then we solve for x by first isolating the term containing x on one side, resulting in y - 7 = 4x, followed by dividing both sides by 4 to get x = (y - 7) / 4. Finally, we switch the variables x and y to get the inverse function: f^{-1}(x) = (x - 7) / 4.