Question

Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) f(x) = x + 3 x2 − 2x − 15

Answer 1

Answer:

  -3 (removable), +5

Step-by-step explanation:

Maybe you have ...

  $f(x)=\dfrac{x+3}{x^2-2x-15}=\dfrac{x+3}{(x+3)(x-5)}=\dfrac{1}{x-5}\quad x\ne-3$

This will have discontinuities (points where the function is undefined) at ...

• x = -3
• x = 5

The discontinuity as x = -3 is removable by defining f(-3) = -1/8.