For each of the functions given identify the value of x for which y= 1/f(x) will have vertical asymptotes
f(x) = x(x-3)
To find the vertical asymptotes for y = 1/f(x), we need to identify the values of x for which f(x) equals zero. This is because a vertical asymptote occurs when the denominator of a function approaches zero.
For f(x) = x(x-3), set the denominator equal to zero and solve for x:
x(x-3) = 0
Setting each factor equal to zero, we have:
x = 0 and x - 3 = 0
Solving for x gives us:
x = 0 and x = 3
Therefore, the vertical asymptotes for y = 1/f(x) occur at x = 0 and x = 3.