# Domain of Function

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Problem #1
What is the domain of $f(x)=x^2-12x+8x^7-3$?

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

Problem #3
What is the domain of $f= \lbrace (1,3),(\sqrt{2},-2),(0,3) \rbrace$?

Problem #4
What value can $k$ have so that the function $h(x)=\frac{x^2-8}{x^2+k}$ has domain $\mathbb{R}$?

Problem #5
What is the domain of $h(x)=\sqrt{\frac{1-x}{x+1}}$?

Problem #6
The domain of $f(x)=\frac{x}{x^2+mx+n}$ is $\mathbb{R} \backslash \lbrace 1 ,2 \rbrace$. Find $m$ and $n$

Problem #7
The range of $f(x)=\frac{x}{\sqrt{x^2-2x-8}}$ is $\lbrace -1, 1 \rbrace$. What is its domain?

Problem #8
If the domain of $g(x)=\frac{1}{\sqrt{x^2-kx+4}}$ is $\mathbb{R}$, what is the value of $k$?

Problem #9
The domain of which one is not $\mathbb{R}$?

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