Question

Find the domain of f/g

Answer 1

Option c. All real numbers except
`x = (3)/(4)`

Step by step explanation:

The first thing we must do is divide the function
`f(x) = 3x ^ 2 + x ^ 4 +2` between the function
`g(x) = 4x-3`

`(f)/(g) = (3x ^ 2 + x ^ 4 +2)/(4x-3)`

Note that both the domain of f(x) and the domain of g(x) are all reals, since they are polynomial functions.

However, remember that the division between zero is not allowed. Therefore now the domain of f(x)/g(x) are all values of x for which the denominator is nonzero. Therefore we must find the values for which g(x) = 0

`4x-3 = 0`

`4x = 3`

`x = (3)/(4)`

Finally the domain of f/g are all real numbers except
`x = (3)/(4)`

Answer 2

Choice C

Explanation:

The domain of a function is defined as the values of x for which the function is real and defined. For a rational function, the function will be defined everywhere except where the function in the denominator assumes a value of zero. In order to determine the points of discontinuity, we solve the equation; 4x-3=0. This yields x = 3/4 as the only singularity point. The domain of the function is thus; all real numbers except 3/4