Find the domain and range of $f ( x ) = \frac { 1 } { \sqrt { x - 3 } }$
A) Domain: $( - \infty , 3 ]$ Range: $[ 0 , \infty )$
B) Domain: $[ 0 , \infty )$ Range: $( - \infty , 3 ]$
C) Domain: $( - \infty , 3 )$ Range: $( 0 , \infty )$
D) Domain: $( 3 , \infty )$ Range: $( 0 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{1}{\sqrt{x-3}}$ is defined for $x > 3$ because the square root requires a non-negative argument, and the denominator cannot be zero. The range is $(0, \infty)$ because as $x$ increases, $f(x)$ approaches 0 but never reaches it, and as $x$ approaches 3 from the right, $f(x)$ increases without bound.

Find the Domain and Range Of f(x)=1x−3f ( x ) = \frac { 1 } { \sqrt { x - 3 } }f(x)=x−3​1​

Find the Domain and Range Of $f ( x ) = \frac { 1 } { \sqrt { x - 3 } }$