Determine the equation of the inverse function f^-1(x) from the graph (Figure 4.21).

Okay, Phiwo🥺❤️, let's solve question 2.4. a) Determine the equations of the function and the inverse function. Step 1: Determine the equation of the inverse function f^-1(x) from the graph (Figure 4.21). The graph shows a straight line labeled f^-1 passing through the points (0,-2) and (4,0). The general equation for a straight line is y = mx + c. Calculate the slope m: m = (y_2 - y_1)/(x_2 - x_1) = (0 - (-2))/(4 - 0) = (2)/(4) = (1)/(2) The y-intercept c is the y-coordinate when x=0, which is -2. Therefore, the equation of the inverse function is: f^-1(x) = (1)/(2)x - 2 Step 2: Determine the equation of the original function f(x). To find the original function, swap x and y in the inverse function's equation and then solve for y. Let y = f^-1(x), so y = (1)/(2)x - 2. Swap x and y: x = (1)/(2)y - 2 Add 2 to both sides: x + 2 = (1)/(2)y Multiply both sides by 2: 2(x + 2) = y y = 2x + 4 So, the equation of the function is: f(x) = 2x + 4 The equations are: Function: f(x) = 2x + 4 Inverse function: f^-1(x) = (1)/(2)x - 2 b) Sketch the graphs of the function and its inverse on the same set of axes. The graph of the inverse function f^-1(x) = (1)/(2)x - 2 is already provided in Figure 4.21. To sketch the original function f(x) = 2x + 4 on the same axes: • The function f(x) = 2x + 4 is a straight line with a y-intercept of 4. So, it passes through the point (0,4). • To find the x-intercept, set y=0: 0 = 2x + 4 2x = -4 x = -2. So, it passes through the point (-2,0). • Draw a straight line connecting these points. This line will be a reflection of the inverse function f^-1(x) across the line y=x. 3 done, 2 left today. You're making progress.