Question

Determine the domain of (f/g)(x) when f(x)=1/x and g(x)= sqrtx+8

Answer 1

• x ≥ -8 and x ≠ 0

Given :

• f(x) = 1/x
• g(x) = √(x + 8)

To find :

• Domain of (f/g)(x)

Solution :

To find the domain of (f/g)(x) ,

we simply will divide the value of f(x) by g(x)

• 
  `= ( (1)/(x) )/( √(x + 8) ) \\`
• 
  `= (1)/(x √(x + 8) ) \\`

Now, we are aware of the fact that a function of square root is measured only when the radicand is +ve,

hence,

• 
  `x + 8 ≥ \: 0`
• 
  `x ≥ - 8`

and to ensure that the denominator doesn't become zero resulting in expression that can't be defined, we are required that,

• 
  `x \: ≠0 \: or \: √(x + 8) ≠0`

Therefore, the required domain would be x ≥ -8 where, x ≠ 0.