Question

Pls help pls helppp i will giving breanlist

Let f (x) = 7+3 and g(x) = Vx+5. What is the domain of (fºg)(x)?

Answer 1

[-5, 4) ∪ (4, ∞)

Explanation:

Given functions:

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

`g(x)=√(x+5)`

Composite function:

`\begin{aligned}(f\:o\:g)(x)&=f[g(x)]\\ & =(1)/(√(x+5)-3) \end{aligned}`

Domain: input values (x-values)

For
`(f\:o\:g)(x)` to be defined:

`x+5\geq 0 \implies x\geq -5`

`√(x+5)\\eq 3 \implies x\\eq 4`

Therefore,
`-5\leq x < 4` and
`x > 4`

⇒ [-5, 4) ∪ (4, ∞)