Find the domain of the function \(\displaystyle f(x) = \sqrt{\ln \left(\frac {4x - x^2}3 \right)}\)
+23246 Because both square roots and natural logs are not defined for negative values, let's find where the
function is zero.
sqrt[ ln[ (4x - x2) / 3 ] ] = 0
---> ln[ (4x - x2) / 3 ] ] = 0 (squaring both sides)
---> (4x - x2) / 3 = e0 (writing as an exponent)
---> (4x - x2) / 3 = 1
---> (4x - x2) = 3
---> -x2 + 4x - 3 = 0
---> x2 - 4x + 3 = 0
---> (x - 1)(x - 3) = 0
---> x = 1 or x = 3
Checking values below 1 results in an undefined situation.
Checking values above 1 results in an undefined situation.
But, values 1 <= x <= 3 work so this is the domain.
