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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)`

Respuesta :

Here [tex] f(x) =2-\sqrt{x} [/tex]

[tex] g(x)=x^{2} -9 [/tex]

[tex] g(x)-f(x) = x^{2} -9-2- \sqrt{x} [/tex]

[tex] g(x)-f(x) =x^{2} -11-\sqrt{x} [/tex]

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 ≥≥≥[tex] x\geq 0 [/tex]

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