Question

which inequality represents all values of x for which the quotient below is defined?√8x^2 divided by √2x

Answer 1

The function is defined when x > 0

Explanation:

Functions with radicals are only undefined when the value in the radical is negative, because the root of a negative number is imaginary.

We know the function is undefined when the denominator is equal to zero.
`√(2x)` is equal to zero when x=0.

We also know that functions with radicals are undefined when the value in the radicals are negative, because the root of a negative number is imaginary. .
`8x^(2)` will always be positive, but
`2x` is negative when x < 0.

So the function is undefined when x = 0, and when x < 0.

Therefore it is defined when x > 0