SOLUTION: This is a polynomial and rational inequality problem. The problem is f(x)= 7x(squared)-59x+24 (the equation has the square root symbol throughout. The question is "what is the d

Algebra ->  Equations -> SOLUTION: This is a polynomial and rational inequality problem. The problem is f(x)= 7x(squared)-59x+24 (the equation has the square root symbol throughout. The question is "what is the d      Log On


   

Question 98069: This is a polynomial and rational inequality problem. The problem is
f(x)= 7x(squared)-59x+24 (the equation has the square root symbol throughout. The question is "what is the domain?"
Answer by mathslover(157) About Me  (Show Source):
You can put this solution on YOUR website!
F(x)= +sqrt%287x%5E2+-59x+%2B24%29
the domain of the function is x such that 7x%5E2+-59x+%2B24+%3E=0
using middle term factorisation
+7x%5E2+-+56x+-+3x+-24+%3E=0
+7x%28x-8%29+-3%28x-8%29+%3E=0
%28x-8%29%287x-3%29%3E=0
Now the left hand side expression of the inequality will be greater than or
equal to 0 when both the factors are greater than or equal to 0 or both of them are less than or equal to zero
so we have
x-8>=0 and 7x-3>=0
x>=8 and x>=3/7
so in effect what it means is that x should be >=8 and x >=3/7
which would combine to give one condition x>=8
also
x-8<=0 and 7x-3<=0
x<=8 and x<=7/3
this would combine to give x<=7/3
so the domain is {x<=7/3} U {x>=8}