Find the domain of x in the following expression. $\sqrt [ 3 ] { x ^ { 4 } - 625 }$
A) $[ - 5,5 ]$
B) $( - \infty , 5 ) \cup ( 5 , \infty )$
C) $[ 5 , \infty )$
D) $( 5 , \infty )$
E)all real numbers

Question

Quizplus · Accepted Answer

The expression inside the cube root, $x^4 - 625$, can take any real value because the cube root function is defined for all real numbers, including negatives. The fourth power of x ensures that the expression inside the cube root will always be real, as any real number raised to an even power results in a non-negative value. Therefore, the domain of x is all real numbers.

Find the Domain of X in the Following Expression x4−6253\sqrt [ 3 ] { x ^ { 4 } - 625 }3x4−625​

Find the Domain of X in the Following Expression $\sqrt [ 3 ] { x ^ { 4 } - 625 }$