For what values of x, if any, does #f(x) = -tan(pi/6-x) # have vertical asymptotes?

1 Answer

Answer:

#f(x)# have Vertical Asymptotes for #x=-pi/3+-n*180#

where #n=0, 1, 2, 3.....#

Explanation:

From the given #f(x)=-tan(pi/6-x)#

Set the angle #(pi/6-x)=pi/2# because #tan (pi/2)=#undefined

Solving for #x#

#x=-pi/3#

and for tangent function the values are the same everytime #pi# or multiples of #pi# are added or subtracted.
Therefore, the function has asymptotes for values of
#x=pi/3+-n*pi# where #n=0, 1, 2, 3,.....#
Examples:

#x=-pi/3#

#x=-(4pi)/3#

#x=(2pi)/3#

#x=(5pi)/3#