Question

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

Answer 1

`a) \ \ \ f(x)= \frac{\big{5x-2}}{\big{x^2-5x+6}} \ \ \ \ \ \ \ \ \ D:\ \big{x^2-5x+6} \\eq 0\\\\x^2-2x-3x+6 \\eq 0\ \ \ \Leftrightarrow\ \ \ x(x-2)-3(x-2) \\eq 0\\\\\Leftrightarrow\ \ \ (x-2)(x-3) \\eq 0\ \ \ \Leftrightarrow\ \ \ x \\eq 2\ \ \ and\ \ \ x \\eq 3\\\\D=R-\{2;\ 3\}\\\\b) \ \ \ g(x)=√(5-2x) \ \ \ \ \ \ D:\ 5-2x \geq 0\ \ \ \Leftrightarrow\ \ \ -2x \geq -5\\\\\ \ \ \Leftrightarrow\ \ \ x \leq 2.5\ \ \ \Rightarrow\ \ \ D=(-\infty;2.5>`