Question

if the function of x is f(x)=1/rootx-5 then find the domain and range​

Answer 1

Answer:

Domain : (5,∞) and Range : (0,∞)

Step-by-step explanation:

\begin{gathered}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)\end{gathered}

f(x)=

x−5

1

To find Domain of the given function :

x−5

>0

⟹x−5>0

⟹x>5

⟹Domain:(5,∞)

\begin{gathered}\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)\end{gathered}

To find Range of the given function :

y=

x−5

1

y

2

=

x−5

1

x−5=

y

2

1

⟹x=

y

2

1

+5

⟹y



=0andy>0

⟹Range:(0,∞)