Question

A) Given that f(x) = 6x
2 − 2x and g(x) = 2x, what is the domain of
f
g
(x)? (1 point) ( )
the set of all real numbers except x =
1
3
the set of all real numbers
the set of all real numbers except x = 0 and x =
1
3
the set of all real numbers except x = 0

Answer 1

To find the domain of the function \( \frac{f}{g}(x) \), we first need to determine where the function \( g(x) \) is equal to zero since division by zero is undefined.

The function given is:

\[ g(x) = 2x \]

Setting \( g(x) \) to zero:

\[ 2x = 0 \]

Solving for \( x \):

\[ x = 0 \]

This means that \( g(x) \) is zero at \( x = 0 \). For the function \( \frac{f}{g}(x) \) to be defined, \( g(x) \) must be non-zero.

The domain of \( \frac{f}{g}(x) \) will be:

- All real numbers except where \( g(x) \) is zero.

Therefore, the domain of \( \frac{f}{g}(x) \) is:

the set of all real numbers except \( x = 0 \).

Thus, the correct answer is:

**the set of all real numbers except \( x = 0 \)**.