Domain of Function

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

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

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

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

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

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

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

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

Problem #9
The domain of which one is not [tex] \mathbb{R} [/tex]?




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