Identify the domain and range of fx 102 3x hx squareroot

Identify the domain and range of: f(x) = 10/(2 - 3x) h(x) = squareroot 5x/(1 - X)^2 g(x) = 4x + 3

Solution

Answer:
1. f(x) = 10/ (2-3x)

Domain is the set of inputs of x such that f(x) makes the sense

2 - 3x > = 0

2 -3x = 0

-3x = -2

3x = 2

x = 2 /3

Thus domain = [ 0 , 2/3]

Range :

f(x) = 10/ (2 - 3x)

   > = 0

   < = 10/2 = 5 , range = [ 0 , 5]

2. h(x) = root ( 5x/(1-x)^2

Domain = 5x/(1-x)^2 > = 0

5x = 0 , x = 0

Domain = [ 0 , 0 ]

Range = [0,0]

3. g(x) = 4x +3

Domain :

4x + 3 > = 0

4x = -3

x = -3/4

Domain = [ -3/4 , 0 ]

Range = [ 0 , 3 ]