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KATRIN_1 [288]
2 years ago
13

Pls help pls helppp i will giving breanlist

Mathematics
1 answer:
GaryK [48]2 years ago
3 0

Answer:

[-5, 4) ∪ (4, ∞)

Step-by-step explanation:

Given functions:

f(x)=\dfrac{1}{x-3}

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

Composite function:

\begin{aligned}(f\:o\:g)(x)&=f[g(x)]\\ & =\dfrac{1}{\sqrt{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

\sqrt{x+5}\neq 3 \implies x\neq 4

Therefore, -5\leq x < 4  and  x > 4

⇒  [-5, 4) ∪ (4, ∞)

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