Final answer:
The inverse of the function f(x) = 2x + 4 is found by swapping x and y and solving for y, resulting in f^-1(x) = (x/2) - 2. Both f(x) and its inverse can be graphed on the same set of axes, with f(x) starting at (0, 4) and f^-1(x) starting at (-4, 0), both functions reflecting across the line y = x.
Step-by-step explanation:
To find the inverse of the function f(x) = 2x + 4, we need to swap the roles of x and y and then solve for y.
- Begin by writing the function as y = 2x + 4.
- Swap x and y to get x = 2y + 4.
- Solve for y: Subtract 4 from both sides to obtain x - 4 = 2y, and then divide both sides by 2 to get y = (x/2) - 2.
The inverse function is therefore f-1(x) = (x/2) - 2. To graph f(x) and f-1(x) on the same axes, follow these steps:
- Label the horizontal axis as x and the vertical axis as f(x) or y.
- Scale both axes appropriately, considering that for f(x), we have a maximum value of f(x) = 10, 0, and f-1(x) will also be a linear function.
- Plot the graph of f(x) as a line starting at point (0, 4) and rising with a slope of 2, up to the domain limit of x = 20.
- Plot the graph of f-1(x) as a line starting at point (-4, 0) and rising with a slope of 1/2.
The graphs of both the function and its inverse will be linear and when graphed will be reflections of each other across the line y = x.