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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