Determine the domain of the function fx square root 3x 47

Determine the domain of the function: f(x) = square root 3x - 4/7 - 2x

Solution

given

f(x) = sqrt [ (3x -4) / (7-2x) ]

domain means the values which x can satisfy the given function

so sqrt can\'t have negative values

so

(3x -4) / (7-2x) > 0

3x -4 > 0

3x > 4

x>4/3

and (7 -2x) is not equal to zero

x is not equal to 7/2

domain: (4/3 infinte) - {7/2}