Question

Find the domain of the given function.

f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.

Answer 1

[-3,2)U(2,∞) domain of the function

Explanation:

We have given function :
`f(x) =(√(x+3))/((x+8)(x-2))`

To find : The domain of the given function

Solution : Domain is where the function is defined

So, we distribute the function,

1)
`f(x) =√(x+3)`

`x\geq-3`

2)
`f(x) =(x+8)(x-2)`

`x<2`

Therefore, the domain of the function

[-3,2)U(2,∞)

or x∈real no. : -3≤x<2

Answer 2

Square of quantity x plus three means : x+3/√
quantity x plus eight means : (x+8)
quantity x minus two means : (x−2)

Therefore : f(x)=x+3 / √(x+8)×(x−2)

R:x≥−3