Question

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

Answer 1

(−∞,2] and [2,∞)

(−∞,4) and (4,∞)

(−∞,2] and [4,∞)

(−∞,−2] and [2,∞)

Answer 2

Can you first write the `g(x)÷f(x)` for me please?

Answer 3

x^2-9÷2-x^1/2

Answer 4

\(\large\color{red}{ \displaystyle f(x)=2−x^{1/2} }\)
\(\large\color{blue}{ \displaystyle g(x)=x^2- 9 }\)

\(\large\color{black}{ \displaystyle g(x)\div f(x)=\frac{\color{blue}{ \displaystyle x^2- 9 } }{\color{red}{ \displaystyle 2−x^{1/2} }} }\)

Answer 5

YOu probably know that:

\(\large\color{black}{ \displaystyle x^{1/2}=\sqrt{x} }\)

Answer 6

Can you take the square root of a number that is smaller than zero?

Answer 7

I am guessing that my interpretation is incorrect... can you write the equation in code or draw to make it clear?

Answer 8

You are correct i got it from here thank you so much for your help !

Answer 9

Whatever you say... yw then