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 ) .

6 cm

step-by-step explanation: