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(i) The domain of a square root are non-negative real numbers.
So, 5 - 2x ≥ 0 ==> x ≤ 5/2.
(ii) The denominator can never equal 0.
So, 5 + 2x ≠ 0 ==> x ≠ -5/2.
By (i) and (ii), the domain for F is {x in R : x ≤ 5/2 and x ≠ -5/2}.
I hope this helps!
So, 5 - 2x ≥ 0 ==> x ≤ 5/2.
(ii) The denominator can never equal 0.
So, 5 + 2x ≠ 0 ==> x ≠ -5/2.
By (i) and (ii), the domain for F is {x in R : x ≤ 5/2 and x ≠ -5/2}.
I hope this helps!