Question

найти область определения функции f(x)=$sqrt{log _{0,3} frac{2x-4}{8-x}$

Answer 1

$f(x)=sqrt{log_{0,3} frac{2x-4}{8-x} }\\ODZ:quad left { {{log_{0,3} frac{2x-4}{8-x} geq 0 } atop { frac{2x-4}{8-x} textgreater 0 }} right. ; left { {{ frac{2x-4}{8-x} leq 1} atop { frac{2(x-2)}{-(x-8)} textgreater 0}} right. ; left { {{ frac{2x-4}{8-x}-1 leq 0 } atop { frac{x-2}{x-8} textless 0}} right. ; left { {{ frac{3x-12}{-(x-8)} leq 0 } atop {frac{x-2}{x-8} textless 0}} right. \\a); ; frac{3(x-4)}{-(x-8)} leq 0; ;; ; ; ---[, 4, ]+++(8)---\\xin (-infty ,4, ]cup (8,+infty )$

$b); ; frac{x-2}{x-8} textless 0; ;; ; +++(2)---(8)+++\\xin (2,8)\\c); ; left { {{xin (-infty ,4, ]cup (8,+infty )} atop {xin (2,8)}} right. ; ; ; Rightarrow ; ; ; xin varnothing$