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**domain and range question!!**

Hi,

I have a quick domain and range question, I have placed my answer below the question. I'm having doubts that it is right! Can someone please help me verify it. Thanks in advance!

_____

Let f(x)= x² + 2 and g(x) =√1-x²

a) Find the domain and range of f and g.

b) Are the functions f.g and g.f defined? Explain?

ANSWER:

The domain of f is {X|X ε R}

The range of f is {y|y ≥ 2, yε R}

f.g= f[g(x)]

= f ___

(√ 1-x²)

= ___

(√ 1-x²) + 2

= 1- x² + 2

= 3-x²

All of the above is correct. I have also already done g.f as well.

This is where i need help....what comes next....

Are the functions f.g and g.f defined? Explain? and what is the domain of g and the range of g?

Thanks in advance for your help!!

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