Give the domain of the following functions. Give your answer in interval notation. a) f(x)= 5x-2/x^2-5x+6 and b) square root of 5-2x

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ReginiaLightfoot706 ReginiaLightfoot706

31-05-2014
Mathematics

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Give the domain of the following functions. Give your answer in interval notation. a) f(x)= 5x-2/x^2-5x+6 and b) square root of 5-2x

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kate200468 kate200468 · Answer 1 · 2014-05-31T02:32:25+02:00

[tex]a) \ \ \ f(x)= \frac{\big{5x-2}}{\big{x^2-5x+6}} \ \ \ \ \ \ \ \ \ D:\ \big{x^2-5x+6} \neq 0\\\\x^2-2x-3x+6 \neq 0\ \ \ \Leftrightarrow\ \ \ x(x-2)-3(x-2) \neq 0\\\\\Leftrightarrow\ \ \ (x-2)(x-3) \neq 0\ \ \ \Leftrightarrow\ \ \ x \neq 2\ \ \ and\ \ \ x \neq 3\\\\D=R-\{2;\ 3\}\\\\b) \ \ \ g(x)=\sqrt{5-2x} \ \ \ \ \ \ D:\ 5-2x \geq 0\ \ \ \Leftrightarrow\ \ \ -2x \geq -5\\\\\ \ \ \Leftrightarrow\ \ \ x \leq 2.5\ \ \ \Rightarrow\ \ \ D=(-\infty;2.5>[/tex]