find the equation of all vertical asymptotes of the following function.\nf(x)=\frac{x - 1}{sqrt{40 - 5x}}

Explanation:

Step1: Recall vertical - asymptote condition

Vertical asymptotes occur where the function is undefined and the denominator approaches 0 while the numerator does not. Set the denominator equal to 0. $\sqrt{40 - 5x}=0$

Step2: Solve the equation for x

Square both sides of the equation to get rid of the square - root: $40−5x = 0$. Then, solve for x: $-5x=-40$ $x = 8$

Answer:

$x = 8$