Find the domain and range of $f ( x ) = \sqrt { x ^ { 2 } - 5 x + 4 }$
A) Domain: $( - \infty , - 4 ) \cup ( - 1 , \infty )$ Range: $( 0 , \infty )$
B) Domain: $( - \infty , 1 ) \cup ( 4 , \infty )$ Range: $[ 0 , \infty )$
C) Domain: $( - \infty , 1 ] \cup [ 4 , \infty )$ Range: $[ 0 , \infty )$
D) Domain: $( - \infty , 1 ] \cup [ 4 , \infty )$ Range: $( 0 , \infty )$

Question

Quizplus · Accepted Answer

The expression inside the square root, $x^2 - 5x + 4$, must be greater than or equal to 0 for the square root to be real. Factoring the quadratic gives $(x-1)(x-4) \geq 0$, which is true for $x \leq 1$ or $x \geq 4$. Thus, the domain is $(-\infty, 1] \cup [4, \infty)$. The range of a square root function is always $[0, \infty)$ because the output of a square root is never negative.

Find the Domain and Range Of f(x)=x2−5x+4f ( x ) = \sqrt { x ^ { 2 } - 5 x + 4 }f(x)=x2−5x+4​

Find the Domain and Range Of $f ( x ) = \sqrt { x ^ { 2 } - 5 x + 4 }$