Find the domain of the real-valued function
f(x) = sqrt(-6x^2 + 25x - 4)
Give the endpoints in your answer as common fractions (not mixed numbers or decimals).
+128475 We must have that
-6x^2 + 25x - 4 ≥ 0 multiply through by -1, reverse the inequality sign
6x^2 - 25x + 4 ≤ 0 factor as
(6x - 1) ( x - 4) ≤ 0
6x - 1 = 0 x -4 = 0
6x =1 x = 4
x= 1/6
Note that we have three intervals to consider (-inf, 1/6] , [ 1/6 , 4] , [4, inf)
The one that is good is [ 1/6, 4 ] = the domain
See the graph, here : https://www.desmos.com/calculator/r6wnwsrerf
