For what values of x, if any, does #f(x) = 1/((2x-3)(7x-3) # have vertical asymptotes?

1 Answer
Feb 7, 2016

Answer:

Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.

Explanation:

In this case the denominator is,
#(2x - 3)(7x - 3)#
now put #(2x - 3)(7x - 3) = 0#
#=># either #(2x - 3) = 0# or #(7x - 3) = 0#
if #(2x - 3) = 0#
then #2x = 3# #=># #x = 3/2#

and if #(7x - 3) = 0#
then #7x = 3# #=># #x = 3/7#

so #x = 3/2# and #x = 3/7# are the vertical asymptotes.