Let `f,\ g` be two real functions defined by `f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot` Then describe each of the following function: `f+g`

Explanation

Given
`f(x)=sqrt(x+1)` and is defined for all `x >=-1`.Thus, domain `(f)=[-1, oo]`.

`g(x)=sqrt(9-x^2)` is defined for `9-x^2>=0=>x^2-9<=0`

`x^2-3^2<=0`

`(x+3)(x-3)<=0`

`x in [-3, 3]`

thus, domain `g-[-3, 3]`.

Now, domain `(f)` `cap` domain `(g)``-``(-1, oo) cap [-3, 3]=[-1, 3]`
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