Answered

IDNLearn.com: Where your questions meet expert advice and community insights. Discover the information you need quickly and easily with our reliable and thorough Q&A platform.

At what x value does the function given below have a hole?

f(x)=x+3/x2−9

Sagot :

Answer:

hole at x=-3

Step-by-step explanation:

The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)

The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.

So anyways we have (x+3)/(x^2-9)

= (x+3)/((x-3)(x+3))

Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.