Question

For what values of x, if any, does `f(x) = 1/((x-4)(x-7))` have vertical asymptotes?

Answer 1

`x=4 or x=7`

Explanation:

Vertical asymptotes: `x-4=0 and x-7=0`

=> `x=4 or x=7`

`lim_(x->4) 1/((x-4)(x-7)) =1/(0*-3) = 1/0 =oo`

`lim_(x->7) 1/((x-4)(x-7)) =1/(3*0) = 1/0 =oo`