Question

50 POINTS!!! i WILL GIVE BRAINLISET IF YOU ANSWER FAST Find the domain for the rational function f of x equals quantity x minus 3 over quantity 4 times x minus 1. (−∞, 3)(3, ∞) (−∞, −3)( −3, ∞) negative infinity to one fourth and one fourth to infinity negative infinity to negative one fourth and negative one fourth to infinity

Answer 1

The third one

Explanation:

Answer 2

`(-\infty,1/4)\cup(1/4,\infty)`

The answer is C.

Explanation:

We are given the rational function:

`\displaystyle f(x) = (x-3)/(4x-1)`

In rational functions, the domain is always all real numbers except for the values when the denominator equals zero. In other words, we need to find the zeros of the denominator:

`\displaystyle \begin{aligned}4x -1 & = 0 \\ \\ 4x & = 1 \\ \\ x & = (1)/(4) \end{aligned}`

Therefore, the domain is all real number except for x = 1/4.

In interval notation, this is:

`(-\infty,1/4)\cup(1/4,\infty)`

The left interval represents all the values to the left of 1/4.The right interval represents all the values to the right of 1/4. The union symbol is needed to combine the two. Note that we use parentheses instead of brackets because we do not include the 1/4 nor the infinities.

In conclusion, our answer is C.