What is the domain of the function: f(x) = 5/(2x^2 - x - 3)?

2 Answers
Sasha P.
Sep 15, 2015

D_f=(-oo,-1)uu(-1,3/2)uu(3/2,+oo)

Explanation:

We have to find the points of discontinuity:
2x^2-x-3=0
2x^2+2x-3x-3=0
2x(x+1)-3(x+1)=0
(x+1)(2x-3)=0
x+1=0 vv 2x-3=0
x=-1 vv x=3/2

D_f=(-oo,-1)uu(-1,3/2)uu(3/2,+oo)

Saurabh Shree
Sep 15, 2015

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 1/0. ,
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 is of the form p//q a Rational function.

A Rational function is defined when
both p and q are defined and q !in0.

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

So
q=0
when
2x^2-x-3=0
2x^2+2x-3x-3=0
2x(x+1)-3(x+1)=0
(x+1)(2x-3)=0
x+1=0 vv 2x-3=0
x=-1 vv x=3/2

D_f=(-oo,-1)uu(-1,3/2)uu(3/2,+oo)

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