Question 98069
F(x)= {{{ sqrt(7x^2 -59x +24)}}}

the domain of the function is x such that {{{7x^2 -59x +24 >=0}}}
using middle term factorisation

{{{ 7x^2 - 56x - 3x -24 >=0}}}
{{{ 7x(x-8) -3(x-8) >=0}}}
{{{(x-8)(7x-3)>=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}