Use set-builder notation and state the domain of these functions?

Question

PLS HELP! 

1. 
   √x 
  ____ 
  4x-9 

2. 

  4√(x+11) 
________ 
       x

Answer 1

(1)

The expression is 

Let the function f(x) = 

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be any negative numbers in the square root.

x ≥ 0

Since there shouldn't be denominator zero.

Denominator = 4x-9 ≠ 0.

4x ≠ 9

x ≠ 9/4

So domain of function is x>=0 and  except at  x = 9/4

Domain = { x ∈ R | x ≥ 0 , x≠9/4 }

Answer 2

(2)

The expression is 

Let the function f(x) = 

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be any negative numbers in the square root.

x+11≥0

x ≥ -11

Since there shouldn't be denominator zero.

Denominator = x ≠ 0.

So domain of function is x≥ -11 and  except at  x = 0

Domain = { x ∈ R | x ≥ -11 , x ≠ 0 }