Question

If `f(x) = 2 - x^(1/2)` and `g(x)=x^2-9`, what is the domain of `g(x)-:f(x)`?

A.
`(-oo,2]` and `[2,oo)`

B.
`[0,4)` and `(4,oo)`

C.
`(-oo,2]` and `[4,oo)`

D.
`(-oo,-2]` and `[2,oo)`

Answer 1

Here
`f(x) =2-√(x)`

`g(x)=x^(2) -9`

`g(x)-f(x) = x^(2) -9-2- √(x)`

`g(x)-f(x) =x^(2) -11-√(x)`

For a radical square-root function, there cannot be a negative number inside the radical. Thus, to find the domain of a radical square root function, we set up the value inside the radical as an inequality greater than or equal to 0 and solve the inequality for the variable.

So domain here would be ≥≥≥
`x\geq 0`