For what values of x, if any, does #f(x) = 1/((x-2)(x-2)(e^x-3)) # have vertical asymptotes?
1 Answer
Jan 28, 2016
Explanation:
Vertical asymptotes occur when the denominator of a function equals
#(x-2)(x-2)(e^x-3)=0#
#(x-2)^2(e^x-3)=0#
Like when factoring and solving a quadratic equation, when we have multiple terms being multiplied by one another and equalling
#(x-2)^2=0#
#x-2=0#
#x=2#
#e^x-3=0#
#e^x=3#
#x=ln3#
The vertical asymptotes occur at