Why this function is undefined at x=0 and x=5 According to my understanding, the domain of sqrt x is x>=0. If this is correct, shouldn't the domain of the function 1(x2−5x)1/4 be x<=0 or x>=5 instead of x<0 or x>5? What am I getting wrong? (the answer is x<0 or x>5).

Jamir Summers

Jamir Summers

Answered question

2022-12-01

Why this function is undefined at x=0 and x=5
According to my understanding, the domain of x is x 0. If this is correct, shouldn't the domain of the function
1 ( x 2 5 x ) 1 / 4
be x 0or x 5instead of x<0 or x>5? What am I getting wrong? (the answer is x<0 or x>5).

Answer & Explanation

Cooper Church

Cooper Church

Beginner2022-12-02Added 9 answers

Note that for
f ( x ) = 1 g ( x )
we need also that
g ( x ) 0
Thus in this case we have
x 2 5 x > 0 x ( x 5 ) > 0 x < 0 x > 5

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