Domain of Function

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Question 1
The domain of a function is the set of all real values for which the function is real valued.

Question 2
If functions f and g have domains [a, b] and [c, d] respectively, then the domain of $\frac{f}{g}$ is given by

Question 3
What is the domain of $$f(x)=x^2-12x+8x^7-3$$?

Question 4
What is the domain of $$g(x)=\sqrt[4]{1-x^2}$$?

Question 5
What value can $$k$$ have so that the function $$h(x)=\frac{x^2-8}{x^2+k}$$ has domain $$\mathbb{R}$$?

Question 6
What is the domain of $$h(x)=\sqrt{\frac{1-x}{x+1}}$$?

Question 7
If the domain of $$g(x)=\frac{1}{\sqrt{x^2-kx+4}}$$ is $$\mathbb{R}$$, what is the value of $$k$$?

Question 8
The domain of which one is not $$\mathbb{R}$$?

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