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

Answer:

(−∞, 2)∪(2, ∞)

Step-by-step explanation:

Domain is all the values that "x" can be

since finding all the values which "x" can be is too hard we will find out the values which "x" can't be- this means equating the denominator to "0" so that the function will be undetermined:

f(x)=\frac{x+1}{x-2}f(x)=

x−2

x+1

since we need the denominator to be "0" we must use the opposite of (-2) which is "2" so we will substitute "2" in the place of "x"f(2)=\frac{2+1}{2-2}f(2)=

2−2

2+1

- the function is now "undetermined" since nothing can be divided by 0 we need to write our answer in proper domain/range format

-Hope this helps!

Answer 2

Answer:

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

The answer is C.

Step-by-step explanation:

So we have the rational function:

$f(x)=\frac{x-3}{4x-1}$

In rational function, the domain is simply all real numbers except for the values when the denominator equals 0. In other words, we need to find the zeros of the denominator. To do this, set the denominator to zero:

$4x-1=0\\x=1/4$

Therefore, the domain is all real numbers except for 1/4.

In interval notation, this is:

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

The left one represents all the values to the left of 1/4.The right 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.