Final answer:
To sketch the graphs of f and f⁻¹ on the same coordinate axes, substitute x-values to find the corresponding y-values for f(x), and substitute y-values to find the corresponding x-values for f⁻¹(x). Connect the points to form the graphs.
Step-by-step explanation:
To sketch the graphs of f and f⁻¹ on the same coordinate axes, we need to understand what the inverse of a function is. The inverse of a function is obtained by interchanging the x and y variables. Let's say f(x) = y, then f⁻¹(y) = x.
To sketch the graph of f, we need to choose several x-values, substitute them into the function, and plot the corresponding y-values. Then, we connect these points to form the graph. To sketch the graph of f⁻¹, we do the same process but substitute y-values and plot x-values.
For example, if f(x) = 2x, we choose x = -1, 0, 1 and find the corresponding y-values: f(-1) = -2, f(0) = 0, and f(1) = 2. Plotting these points, we obtain a straight line representing f(x).
Next, we need to find the inverse function f⁻¹(x). In this example, the inverse function is f⁻¹(x) = x/2. Choosing y = -2, 0, 2 and finding the corresponding x-values: f⁻¹(-2) = -1, f⁻¹(0) = 0, and f⁻¹(2) = 1, we can plot these points on the graph to represent f⁻¹(x).