perplexus.info :: Calculus : A Funny Function

A Funny Function (Posted on 2013-08-01)

Suppose f is a continuous function such that f(1000)=999 and f(x) · f(f(x)) = 1 for all real x. What is f(891)?

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 4.0000 (1 votes)

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Crucial distinction

| Comment 3 of 7 |

If f(x) = 1/x, then the inverse relationship applies across the entire domain.

But we are told that f(f(x)) = 1/f(x).

Let y = f(x). Then the domain of y is the range of x.

Then f(y) = 1/y, if y is in the range of f(x)

Posted by Steve Herman on 2013-08-02 13:58:47

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