If f(x) and its inverse function,f-1(x), are both plotted on the same coordinate plane, where is their point of intersection?
2 answers:
Consider f, such that f(x)=y, where x is in the Domain of f, and y is in the Range of f.
Let f(a)=b. So, (a, b) is in the graph of f.
The inverse function of f,
(if exists) is such that if f(x)=y, then 
.
So if (a, b) is a particular point in the graph of f, then (b, a) is a point in the graph of.
A point where they intersect is a point where (a, b)=(b, a), that is a=b. Among our choices, only (2, 2) satisfies this condition.
Answer: (2, 2)
Let f(a)=b. So, (a, b) is in the graph of f.
The inverse function of f,
So if (a, b) is a particular point in the graph of f, then (b, a) is a point in the graph of
A point where they intersect is a point where (a, b)=(b, a), that is a=b. Among our choices, only (2, 2) satisfies this condition.
Answer: (2, 2)
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Answer:
The equations have the same slope but different y-intercepts. This means the lines are parallel and there is no solution (since they do not intersect).
