Question

find the domain and range=1/root x-5?

Answer 1

above is your answer.

Answer 2

Answer:

Domain : (5,∞) and Range : (0,∞)

Step-by-step explanation:

$f(x) = \frac{1}{\sqrt{x-5}}\\\\\text{To find Domain of the given function : }\\\\\sqrt{x-5}>0\\\implies x-5>0\\\implies x>5\\\bf\implies Domain : (5,\infty)$

$\text{To find Range of the given function :}\\\\y = \frac{1}{\sqrt{x-5}}\\\\y^2=\frac{1}{x-5}\\\\x-5=\frac{1}{y^2}\\\\\implies x=\frac{1}{y^2}+5\\\\\implies y\neq 0\thinspace and\thinspace y>0\\\\\bf\implies Range : (0,\infty)$