We are given the following expression
[tex]\sqrt{28(x-1)}\div\sqrt{8x^2}[/tex]
Let us find out for which values of x the above expression is defined.
Notice that x cannot be 0 since it will make the denominator 0 and the expression will be undefined.
Also, notice that x cannot be less than 0 since it will make the numerator negative and the expression will be undefined.
So, options A and D are straightaway incorrect.
Let us check if the expression is defined for x = 1
[tex]\sqrt{28(1-1)}\div\sqrt{8(1)^2}=0\div\sqrt{8}=0[/tex]
As you can see, the expression is defined for x = 1
We already know that the expression is defined for all values of x greater than 1.
The given expression is defined for all values of x equal to or greater than 1.
Therefore, the correct answer is option C.
