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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).

 Mar 12, 2021
 #1
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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

 

 

cool cool cool

 Mar 12, 2021

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