Question

Let f(x) = 2x2 + x − 3 and g(x) = x − 1.

Find f(x)/g(x) and state its domain

Answer 1

We have 2x^2 + x - 3 = 2x^2 - 2x + 3x - 3 = 2x ( x - 1 ) - 3( x - 1 ) = ( x - 1 )( 2x - 3 );

But g(x) is not 0; then, x is not 1;

The domain is R - {1} ;

f(x) / g(x) = ( x - 1 )( 2x - 3 ) / (x - 1 ) = 2x - 3;

Answer 2

The domain of
`(f(x))/(g(x))` is
`-\infty \:<x<\infty \:`

Explanation:

We need to find the domain of
`(f(x))/(g(x))`

The given functions are:
`f(x)=2x^(2)+x-3` and
`g(x)=x-1`

First, we factorize the f(x);

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

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

`f(x)=2x(x- 1) +3(x -1)`

`f(x)=(2x +3)(x- 1)`

Now, divide f(x) by g(x),

`(f(x))/(g(x))`

`(f(x))/(g(x))=((2x +3)(x- 1))/((x- 1))`

simplify,

`(f(x))/(g(x))=(2x +3)`

`-\infty \:<x<\infty \:`

Therefore, the domain of
`(f(x))/(g(x))` is
`-\infty \:<x<\infty \:`