What is the domain of #g(x)=(5x)/(8x^2-2x-3)#?

1 Answer
Narad T.
Nov 4, 2016

The domain is #RR-(-1/2,3/4)#

Explanation:

The domain depends when #8x^2-2x-3=0#
To solve this equation, we calculate #Delta=b^2-4ac#
#Delta=4+4*8*3#
#Delta=100>0#
#:. # there are 2 real roots
the roots are #x_1=(2+10)/16=3/4#
and #x_2=(2-10)/16=-1/2#
So it's not possible for #x=-1/2# and #x=3/4#
The domain is #RR-(-1/2,3/4)#

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