х+2 f(x) х2 — Зх — 10

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter6: Fractions
Section6.1: Simplifying Fractions
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Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

х+2
f(x)
х2 — Зх — 10
Transcribed Image Text:х+2 f(x) х2 — Зх — 10
Expert Solution
Step 1:Given

f(x)=x+2x2-3x-10

Finding the x value at which function is not continuous . 

And which of the discontinuities are removable.

Step 2:Factoring denominator and checking for the discontinuity

To factor denominator, we need two factors of -10 whose sum is -3

And those two factors are -5 and 2, therefore

f(x)=x+2(x-5)(x+2)

A rational function is undefined when the denominator is 0. So the discontinuity is at that x value which makes the denominator 0.

That is

x-5=0, x+2=0x=-2,5

So the x value of discontinuities are

x=-2,5

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