Question

For what values of x, if any, does `f(x) = sec((-11pi)/8-7x)` have vertical asymptotes?

Answer 1

`x=(2npi)/7 -(7pi)/56 or (2npi)/7-(15pi)/56` , where n= 0,1,2.....

Explanation:

f(x)=`sec(-(11pi)/8 -7x)= sec((11pi)/8 +7x)= 1/(cos((11pi)/8 +7x))`

Vertical asymptotes would occur for values of x obtained on solving the equation `cos((11 pi)/8 +7x) = 0`

That means `(11 pi)/8 +7x = pi/2 or -pi/2`

`7x=2npi -(7pi)/8 or2npi-(15pi)/8`

x=(2npi)/7 -(7`pi)/56 or (2npi)/7-(15pi)/56` , where n= 0,1,2.....

For all the values of x there would be vertical asymptotes for the give function