Final answer:
The y-intercept of the inverse function, f^-1(x), is -16.
Step-by-step explanation:
The y-intercept of the inverse function, denoted as f-1(x), is the point where the inverse function intersects the y-axis. To find the y-intercept of f-1(x), we need to find the x-intercept of f(x).
To find the x-intercept of f(x), we set f(x) equal to zero and solve for x. So, we have 3/4x + 12 = 0.
Solving for x, we get 3/4x = -12. Dividing both sides by 3/4 gives x = -12 * 4/3 = -16. Therefore, the x-intercept of f(x) is -16.
Now, to find the y-intercept of f-1(x), we need to swap the x and y values of the x-intercept of f(x). So, the y-intercept of f-1(x) is -16.