What is the domain of the function: $f (x) = \frac{5}{2 x^{2} - x - 3}$ $f(x) = 5/(2x^2 - x - 3)$ ?

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What is the domain of the function: $f (x) = \frac{5}{2 x^{2} - x - 3}$ $f(x) = 5/(2x^2 - x - 3)$ ?

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Answer 1 · 2015-09-15T16:53:59

$D_{f} = (- \infty, - 1) \cup (- 1, \frac{3}{2}) \cup (\frac{3}{2}, + \infty)$ $D_f=(-oo,-1)uu(-1,3/2)uu(3/2,+oo)$

Explanation:

We have to find the points of discontinuity:
$2 x^{2} - x - 3 = 0$ $2x^2-x-3=0$
$2 x^{2} + 2 x - 3 x - 3 = 0$ $2x^2+2x-3x-3=0$
$2 x (x + 1) - 3 (x + 1) = 0$ $2x(x+1)-3(x+1)=0$
$(x + 1) (2 x - 3) = 0$ $(x+1)(2x-3)=0$
$x + 1 = 0 \lor 2 x - 3 = 0$ $x+1=0 vv 2x-3=0$
$x = - 1 \lor x = \frac{3}{2}$ $x=-1 vv x=3/2$

$D_{f} = (- \infty, - 1) \cup (- 1, \frac{3}{2}) \cup (\frac{3}{2}, + \infty)$ $D_f=(-oo,-1)uu(-1,3/2)uu(3/2,+oo)$

Answer 2 · 2015-09-15T22:15:44

$D_{f} = (- \infty, - 1) \cup (- 1, \frac{3}{2}) \cup (\frac{3}{2}, + \infty)$ $D_f=(-oo,-1)uu(-1,3/2)uu(3/2,+oo)$

Explanation:

First of All we need to know the Meaning of Domain:

A Domain is a set of inputs for which the function gives output
which is not indeterminate or invalid. For Example $\frac{1}{0}$ $1/0$ . ,
$\frac{\infty}{\infty}$ $oo/oo$ etc are indeterminate or invalid forms .

You can find the list of indeterminate forms here .

In Other Words Domain is the set of values for which the function is defined.

Here the function $F_{x}$ $F_x$ is of the form $p / q$ $p//q$ a Rational function.

A Rational function is defined when
both $p$ $p$ and $q$ $q$ are defined and $q \notin 0$ $q !in0$ .

Considering the $F_{x}$ $F_x$ given.We have to find values where the $F_{x}$ $F_x$ gives valid output and which excludes the value where $q$ $q$ becomes $0$ $0$ and give rise to invalid form .

So
$q = 0$ $q=0$
when
$2 x^{2} - x - 3 = 0$ $2x^2-x-3=0$
$2 x^{2} + 2 x - 3 x - 3 = 0$ $2x^2+2x-3x-3=0$
$2 x (x + 1) - 3 (x + 1) = 0$ $2x(x+1)-3(x+1)=0$
$(x + 1) (2 x - 3) = 0$ $(x+1)(2x-3)=0$
$x + 1 = 0 \lor 2 x - 3 = 0$ $x+1=0 vv 2x-3=0$
$x = - 1 \lor x = \frac{3}{2}$ $x=-1 vv x=3/2$

$D_{f} = (- \infty, - 1) \cup (- 1, \frac{3}{2}) \cup (\frac{3}{2}, + \infty)$ $D_f=(-oo,-1)uu(-1,3/2)uu(3/2,+oo)$

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What is the domain of the function: $f (x) = \frac{5}{2 x^{2} - x - 3}$ $f(x) = 5/(2x^2 - x - 3)$ ?

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