Question

Find the domain of f/g

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

A. All real numbers
B. All real numbers except 4/3
C. All real numbers except 3/4
D. (-3,4) U [4, -3)

Answer 1

C. All real numbers except 3/4

Explanation:

We are given

`f(x)=3x^2+x^4+2`

`g(x)=4x-3`

Firstly, we will find f/g

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

Domain:

We know that domain is all possible values of x for which any function is defined

so, we know that denominator of any function can not be zero

so, firstly we set denominator =0

and then we can solve for x

`4x-3=0`

Add both sides by 3

`4x-3+3=0+3`

`4x=3`

`x=(3)/(4)`

so, this function is defined for all values of x except at

`x=(3)/(4)`

Domain will be

All real numbers except 3/4