Question

I need help on this question pls answer :(

Answer 1

Option 3

Explanation:

Given functions are,

f(x) =
`(1)/(x-3)`

g(x) =
`√(x+5)`

Therefore, composite function (f o g) will be,

(f o g)(x) = f[g(x)]

=
`(1)/(√(x+5) -3)`

This function will be defined for,

Denominator > 0

`√(x+5)-3>0`

`√(x+5) >3`

`(x+5)>3^2`

`x+5>9`

`x>9-5`

`x>4`

And
`x+5\geq 0`

`x\geq -5`

Therefore, domain of the composite function will be,

[-5, 4) ∪ (4, ∞)

Option 3 will be the answer.