Question

HEEELP

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)

Answer 1

its d

Explanation:

i did the iready diagnostic test. :)

Answer 2

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.