Dear student,

Let's see the denominator where it is not defined.

So, the function is not defined when the denominator becomes zero. So in order to find the domain we have to make sure that function doesn't lie in the range or satisfy that number which makes the function not defined.

So, the function will be defined only when:-

{x+1/2} + (x-3/2) -7 not equal to zero.

This implies, 2x-1-7 not equal to zero.

This implies that x must not be equal to 4.


Therefore the domain is R - {4}

Or in words it can be said that, the domain of this function is - all real numbers except 4.