Question

I need help on this question pls answer :(

Answer 1

Answer:

Option 3

Step-by-step explanation:

Given functions are,

f(x) = $\frac{1}{x-3}$

g(x) = $\sqrt{x+5}$

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

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

             = $\frac{1}{\sqrt{x+5} -3}$

This function will be defined for,

Denominator > 0

$\sqrt{x+5}-3>0$

$\sqrt{x+5} >3$

$(x+5)>3^2$

$x+5>9$

$x>9-5$

$x>4$

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.