The point (5,-2) lies on the graph of y=f(x), and assume f^-1(x) exists. Find the corresponding point on eAch graph.
A). Y=f^-1(x)
I get (-5,2)
B). Y=-f^-1(-x)+4
I get (5,2)
C). Y=f^-1(x+2)+3
I get (-7,5)
Did I get these right?
To verify if you got the correct points, let's go through each question one by one and determine the corresponding points.
A. Y = f^(-1)(x)
Since (5,-2) lies on the graph of y = f(x), the corresponding point on the inverse graph, y = f^(-1)(x), will have the coordinates flipped. So, the point will be (-2,5) instead of (-5,2). It seems there was a mistake, and the correct answer is (-2,5).
B. Y = -f^(-1)(-x) + 4
Again, since (5,-2) lies on y = f(x), we need to find the corresponding point on y = -f^(-1)(-x) + 4. To get the point, we take the flipped coordinates from the original graph and apply them to the inverse graph. Therefore, the corresponding point to (5,-2) on y = -f^(-1)(-x) + 4 is (5,2). You got this one right!
C. Y = f^(-1)(x+2) + 3
Similar to the previous cases, we need to determine the corresponding point on y = f^(-1)(x+2) + 3 for the given point (5,-2). To get the point, we take the flipped coordinates, (-2,5), and add 2 to the x-coordinate and 3 to the y-coordinate. Thus, the corresponding point is (-2+2, 5+3) = (0,8). It appears your answer for this one is incorrect.
Therefore, the correct answers are:
A. Y = f^(-1)(x): (-2,5)
B. Y = -f^(-1)(-x) + 4: (5,2)
C. Y = f^(-1)(x+2) + 3: (0,8)