Question

Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x)/g(x) and state its domain

Answer 1

Answer:

The domain of $\frac{f(x)}{g(x)}$ is $-\infty \:$

Step-by-step explanation:

We need to find the domain of $\frac{f(x)}{g(x)}$

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),

$\frac{f(x)}{g(x)}$

$\frac{f(x)}{g(x)}=\frac{(2x +3)(x- 1)}{(x- 1)}$

simplify,

$\frac{f(x)}{g(x)}=(2x +3)$

$\mathrm{Domain\:definition}$

$\mathrm{The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values\:for\:which\:the\:function\:is\:real\:and\:defined}$

$\mathrm{The\:function\:has\:no\:undefined\:points\:nor\:domain\:constraints.\:\:Therefore,\:\:the\:domain\:is}$

$-\infty \:$

Therefore, the domain of $\frac{f(x)}{g(x)}$ is $-\infty \:$

Answer 2

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;