SOLUTION: What is the range of the function f(x) = sqrt(5 - 8x + x^2)?

Quadratic function g(x) = 5 - 8x + x^2  has the discriminant

    d = b^2 - 4ac = (-8)^2 - 4*1*5 = 64 - 20 = 44.

The discriminant is positive, which means that this quadratic function has zeroes
that are its y-interceptions.


For us, it means that zero is in the range of the function f(x).
Moreover, since  sqrt()  is, by the agreement, a non-negative function, we conclude that 
the range of f(x) starts from 0 (zero) and goes up to the positive domain.


Next, since the coefficient at x^2 of function g(x) is positive 1, it tells that
function g(x) is unbounded and goes to infinity as x goes to +/- infinity.  
Hence, function f(x) goes to infinity as x goes to +/- infinity.


Combining it, we conclude that the range of f(x) is the set [0,infinity).