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`f(x)= sqrt(x + 9) `
`g(x)= x^2 + 4x -6`
`==gt fog(x)= f(g(x)) = f(x^2+4x-6)= sqrt(x^2+4x-6+9) = sqrt(x^2+4x+3)`
Now we will find the domain.
For the composite function we need to include the domain of the composite function and the input function.
==> First we will find the domain of `fog(x)= sqrt(x^2+4x+3)`
==> The domain are the real numbers such the function is not defined.
==> fog(x) is not defined when `x^2+4x+3 gt 0`
==> (x+3)(x+4) > 0
==> x >-3 and x>-4
`==gt x in (-3,oo)`
==> (x+3) < 0 and (x+4) < 0
`==gt x lt -3 and x lt -4 `
`==gt x in (-oo, -4) `
`==gtx in (-oo,-4)U(-3,oo)`
Also, we need to include the domain of the input function g(x).
The domain of g(x) is all real numbers.
==> Then, we conclude that the domain of fog(x) is the interval:
`x in (-00,-4)U(-3,oo).`
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