Find any points of discontinuity for the rational function.
y=x−8x2+6x−7
To find any points of discontinuity for the rational function y = x/(1 - 8x^2 + 6x - 7), we need to find where the denominator is equal to zero because division by zero is undefined.
Setting the denominator equal to zero:
1 - 8x^2 + 6x - 7 = 0
-8x^2 + 6x - 6 = 0
Now, we can use the quadratic formula to find the solutions for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-(6) ± sqrt((6)^2 - 4(-8)(-6))) / 2(-8)
x = (6 ± sqrt(36 - 192)) / -16
x = (6 ± sqrt(-156)) / -16
x = (6 ± 2i√39) / -16
x = (3 ± i√39) / -8
Therefore, the points of discontinuity for the rational function occur at x = (3 + i√39) / -8 and x = (3 - i√39) / -8. These are the points where the denominator equals zero.