perplexus.info :: Just Math : Find the real function, Get the value

Find the real function, Get the value (Posted on 2023-10-12)

Let f(x) be a real valued function for all x≥0.25, such that:
f(x-√x +1) = √x

Find f(21/16)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Analytical solution (spoiler)

| Comment 1 of 3

x-√x +1 = 21/16

Let y =√x, which is the answer to the puzzle.

Then y^2 - y - 5/16 = 0

Using the quadratic formula,

y = (1 +/- sqrt (1 + 20/16))/2 = 1/2 +/- 3/4

The positive value is 5/4, and that is f(21/16).

Edited on October 12, 2023, 11:03 am

Posted by Steve Herman on 2023-10-12 11:02:42

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