Which answer includes a function, its inverse, and a dashed line that verifies the relationship?
2 answers:
The graphics that are missing can be found in the attachment.
Answer: Graphic of alternative D.
Step-by-step explanation: An inverse function is one that reverses another function: Typically, x denotes the variable while y is the function. In the case of an inverse function, y takes on the variable role and x becomes the function. For example, f(x) = y if and only if g(y) = x.
The graphic depicting an inverse function represents the reflection of the original function across the identity line y=x.
In each alternative provided in the image, the graphs illustrate a function paired with its inverse, however, in alternative D, the dashed line accurately represents the identity line y = x and its correlation with the function and its inverse. Therefore, Graph D is the valid option.
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A="b is situated in the center"
B="c lies to the right of b"
C="The letters def occur sequentially in that arrangement"
a) b can occupy 7 positions; however, only one of these is the center. Therefore, P(A)=1/7
b) Let X=i; "b holds the i-th position"
Y=j; "c occupies the j-th position"
P(B)=1/2
c) Let X=i; "d holds the i-th position"
Y=j; "e occupies the j-th position"
Let Z=k; "f is in the i-th position"
P(C)=1/42
P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420
P(B∩A)=3*(1/7*1/6)=1/14
P(A|C)=P(A∩C)/P(C)=(1/420)/(1/42)=1/10
P(B|C)=P(B∩C)/P(C)=(1/420)/(1/42)=1/10
P(A|B)=P(B∩A)/P(B)=(1/14)/(1/2)=1/7
P(A∩B)=1/14
P(A)P(B)=(1/7)*(1/2)=1/14
Events A and B are independent
P(A∩C)=1/420
P(A)P(C)=(1/7)*(1/42)=1/294
Events A and C are not independent
P(B∩C)=1/420
P(B)P(C)=(1/2)*(1/42)=1/84
Events B and C are not independent