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?
say y = x - 7
(5,-2) lies on that graph
for f^-1
x = y - 7
y = x + 7
if x = 5 then y = 12
so I get
(5,12)
say y = x - 7
(5,-2) lies on that graph
for f^-1
x = y + 7
y = x - 7
if x = 5 then y = -2
so I get
(5,-2)
B. My f^-1(x) = x-7
Y=-f^-1(-x)+4
Y = (-5-7) + 4
Y = -12+ 4 = -8
(5,-8)
C.Y=f^-1(x+2)+3
x+2 = 7
f^-1(7) = 7-7 = 0
Y = 0 + 3 = 3
To determine if you got the points on the graphs correctly, we can go through the process of finding the corresponding points step by step.
A) Y = f^(-1)(x):
To find the corresponding point on the graph of Y = f^(-1)(x), we need to switch the x and y coordinates of the point (5,-2). Therefore, the corresponding point would be (-2, 5), not (-5,2).
B) Y = -f^(-1)(-x) + 4:
To find the corresponding point on the graph of Y = -f^(-1)(-x) + 4, we again need to switch the x and y coordinates of the point (5,-2). However, there is also a negation and a translation involved.
First, let's find the x coordinate:
x = -2 (the original y coordinate)
Then, we apply the negation and get:
-x = -(-2) = 2
Now, let's find the y coordinate:
y = 5 (the original x coordinate)
Then, we apply the inverse function -f^(-1) and get:
-f^(-1)(-x) = -f^(-1)(-2)
Since we don't know the exact function f(x) or its inverse, we can't calculate -f^(-1)(-2) directly. Therefore, we can't determine the corresponding y coordinate for the given x coordinate.
C) Y = f^(-1)(x+2) + 3:
To find the corresponding point on the graph of Y = f^(-1)(x+2) + 3, we need to switch the x and y coordinates of the point (5,-2), and also apply a translation.
First, let's find the x coordinate:
x = -2 (the original y coordinate)
Then, we apply the translation by adding 2:
x + 2 = -2 + 2 = 0
Now, let's find the y coordinate:
y = 5 (the original x coordinate)
Then, we switch the x and y coordinates and find f^(-1)(x):
f^(-1)(x) = f^(-1)(5)
Just like in the previous case, since we don't know the exact function f(x) or its inverse, we can't calculate f^(-1)(5) directly. Therefore, we can't determine the corresponding y coordinate for the given x coordinate.
In conclusion, you didn't get these points right because the functions f(x) and its inverse f^(-1)(x) are not provided, making it impossible to find the corresponding points accurately.