For the square root and the division, the conditions are
#(-x^2+5x-4)>0# and #x!=1# and #x!=4#
Let #f(x)=(-x^2+5x-4)=-(x^2-5x+4)=-(x-1)(x-4)#
We can build the sign chart
#color(white)(aaaa)##x##color(white)(aaaaaaa)##-oo##color(white)(aaaaaa)##1##color(white)(aaaaaaaa)##4##color(white)(aaaaaa)##+oo#
#color(white)(aaaa)##-(x-1)##color(white)(aaaaa)##+##color(white)(aaa)##||##color(white)(aaa)##-##color(white)(aaaaaa)##-#
#color(white)(aaaa)##(x-4)##color(white)(aaaaaaa)##-##color(white)(aaa)####color(white)(aaaa)##-##color(white)(aa)##||##color(white)(aaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaaaaaa)##-##color(white)(aa)##||##color(white)(aaa)##+##color(white)(aa)##||##color(white)(aaa)##-#
Therefore,
#f(x)>0#, when #x in (1,4)#
graph{1/sqrt(-x^2+5x-4) [-9.55, 18.93, -4.48, 9.76]}