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let f(x) =1/x-3 and g(x)=√x+5. What is the domain of (f o g)(x)

Options

a) [-5,-4)U(-4, inf)

b) [-5,-3)U(-3,inf)

c)[-f,4)U(4,inf)

d)[-5,3)U(3,inf)

User Isedwards
by
8.4k points

2 Answers

2 votes

Answer:

its d

Explanation:

i did the iready diagnostic test. :)

User Adrian Moisa
by
8.0k points
2 votes

Answer: (c)

Explanation:

Given


f(x)=(1)/(x-3)\\\\g(x)=√(x+5)

Here,
√(x+5)\ \text{is always greater than equal to 0}\\\Rightarrow x+5\geq 0\\\Rightarrow x\geq -5\quad \ldots(i)

To get
f\left(g(x)\right), replace
x in
f(x) by
g(x)\ \text{i.e. by}\ √(x+5)


\Rightarrow f\left(g(x)\right)=(1)/(√(x+5)-3)\\\\\text{Denominator must not be equal to 0}\\\\\therefore √(x+5)-3\\eq0\\\Rightarrow √(x+5)\\eq 3\\\Rightarrow x+5\\eq 9\\\Rightarrow x\\eq 4\quad \ldots(ii)

Using
(i) and
(ii) it can be concluded that the domain of
f\left(g(x)\right) is all real numbers except 0.

Therefore, its domain is given by


x\in [-5,4)\cup (4,\infty)

Option (c) is correct.

User PracticalGuy
by
8.2k points
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