Find the domain of the function f (x) = the square root of 6 - the square root of 2x + 7

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).