Question

Find all vertical asymptotes of (g/f)(x)
g(x)= square root of x-15 (all under square root)
f(x)=x^2-2x

Answer 1

\[\left(\frac{g}{f}\right)(x) = \frac{\sqrt{x-15}}{x^2-2x}\]Vertical asympttes tell you the restrictions to your functions. They are found by setting the denominator = 0. \[x^2-2x=0\]\[x(x-2)=0\]\[x=? \\ x-2=0 \iff x=~?\]

Answer 2

x=0 and x=2? does the x under the square root matter at all? @Jhannybean

Answer 3

No because if x = 15, then our function would = 0, which is perfectly ok.

Answer 4

Thanks!