Question

Question 14, pre calc, I am at work so please finish question so when I get home I can review it, thanks!

Answer 1

Given the question in the image, the following are the solution steps to get the discontinuity of the function

Step 1: Write the given function

`f(x)=(2x^2+3x-5)/(\left(x-1\right)\left(x+5\right))`

Step 2: Define discontinuity of a function

A function has a removable discontinuity at x=a if

`\begin{gathered} \lim _(x\to a)(f(x))\text{ exi}sts\text{ and is finite} \\ \end{gathered}`

f(x) has step discontinuity if one-sided limits exist and finite but not equal.

f(x) has infinite discontinuity if one or both of the one-sided limits don't exist or are infinite

Step 3: State the infinite discontinuity and the removable discontinuity

To get the removable discontinuity

`\begin{gathered} x-1=0 \\ x=0+1 \\ x=1 \end{gathered}`

To get the infinite discontinuity

`\begin{gathered} x+5=0 \\ x=0-5 \\ x=-5 \end{gathered}`

Hence, the discontinuity is removable at x=1 and infinite at x=-5

Option D