Let f(x) be a real valued function for all x≥0.25, such that:
f(x-√x +1) = √x
Find f(21/16)
Oh, were we supposed to find the function? The problem does not ask for it, but the problem title does.
Let y=sqrt(x)
Let z = x - sqrt(x) +1
Substituting, z = y^2 - y + 1
0 = y^2 - y + (1-z)
Solve for y using the quadratic function
y = 1/2 + sqrt(z - 3/4)
So, f(z) = 1/2 + sqrt(z - 3/4), and that is the function.
And then, f(21/16) = 5/4.
Unfortunately, the problem has an error. The desired function is only real-valued for x >= 0.75, not x >= 0.25
Finding the function (spoiler)
