Given function is
f(x) = √(6) - √ ( 2x + 7) .
We have to find domain .
Domain of a function is the set of all x values for which the function is real and defined .
Here we have a square root function .
Square root function can not be negative . These are real and defined for positive radicals only .
Thus we need to find non negative value for radical .
Square root 6 is constant term .
We need to look for x values for square root 2x + 7 .
Set 2x + 7 ≥ 0
Subtracting 7 from both sides , we get
2x ≥ - 7
Divide by 2 , we get
x ≥ - 7/2
Thus domain of the given function is all values greater than or equal to x = -7/2 .
In interval notation , domain of f(x) is [ - 7/2 , infinity ) or [ -3.5, infinity ) .