Find the intervals on which the function is continuous.
-$$y = \sqrt [ 4 ] { 2 x - 4 }$$
A) continuous on the interval $( - \infty , 2 ]$
B) continuous on the interval $( 2 , \infty )$
C) continuous on the interval $[ 2 , \infty )$
D) continuous on the interval $[ - 2 , \infty )$

Question

Quizplus · Accepted Answer

The function is defined under the square root only if $2x-4 \geq 0$, i.e. $x \geq 2$. Therefore, the function is not defined on the interval $(-\infty,2)$. However, for any $x \geq 2$, the function is continuous because it is the composition of the continuous functions $x \mapsto 2x-4$ and $x \mapsto \sqrt[4]{x}$. Therefore, the function is continuous on the interval $[2,\infty)$.

Find the Intervals on Which the Function Is Continuous y=2x−44y = \sqrt [ 4 ] { 2 x - 4 }y=42x−4​

Find the Intervals on Which the Function Is Continuous $y = \sqrt [ 4 ] { 2 x - 4 }$