The function f is one-to-one. Prove that the sum of all the x- and y-intercepts of the graph of f(x) is equal to the sum of all the x- and y-intercepts of the graph of f^(−1)(x).

Alexia Avila

Alexia Avila

Answered question

2022-11-13

The function f is one-to-one. Prove that the sum of all the x- and y-intercepts of the graph of f ( x ) is equal to the sum of all the x- and y-intercepts of the graph of f 1 ( x ).

Answer & Explanation

lesinetzgl5

lesinetzgl5

Beginner2022-11-14Added 18 answers

We have the sum x 1 + f ( 0 ) , where f ( x 1 ) = 0 and let's say f ( 0 ) = y 1 .
This means that f 1 ( 0 ) = x 1 and f 1 ( y 1 ) = 0. This means that x 1 is the y-intersept of f 1 ( x ) and that y 1 is its x-intersept.
If we count the x- and y-intersept of f 1 ( x ) in the same way we did for f ( x ), we get
y 1 + f 1 ( 0 ) = f ( 0 ) + x 1 ,
which is the same sum indeed.

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