Question

For what values of x, if any, does `f(x) = 1/((x-2)(x+2)(e^x-1))` have vertical asymptotes?

Answer 1

`x=+-2, x=0`

Explanation:

Vertical asymptotes occur whenever the denominator of a rational function equals zero. In this case, one of the three binomials in the denominator must equal zero.

1. `(x-2)=0 => x=2`

2. `(x+2)=0 => x=-2`

3. `(e^x-1)=0 => e^x=1 => x=ln(1)=0`