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

Question

1361 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-14T15:47:03

$x=4 or x=7$

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

=> $x=4 or x=7$

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

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

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