Question

Define the function f (x) at 1 so that it becomes continuous at 1 - given the attached.

Answer 1

Multiply by the conjugate of the top. That will help you get rid of x-1 in the denominator.

Answer 2

I got when f(1)=0

Answer 3

I think the answer should be 1/4.

\[\frac{\sqrt{x+3}-2}{x-1} \cdot \frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}\]

Answer 4

\[= \frac{1}{\sqrt{x+3}+2}\]
Then
\[f(1) = \frac{1}{4}\]

Answer 5

why would you want to remove a radical from the numerator and put it in the denom?

Answer 6

To make the function continuous you want the limit and the evaluation to be the same number.

Answer 7

gotcha!

Answer 8

so wouldn't f(1)=0 also work, though?

Answer 9

How are you getting 0? Are you plugging it in to the original function?

Answer 10

or is it discontinuous at that point?

Answer 11

im plugging in the 1

Answer 12

That causes 0 in the denominator. We can't divide by 0.

Answer 13

oooo i see my mistake

Answer 14

thank you!!!!

Answer 15

That was all you!

Answer 16

the next q I posted; im trying to see if it has a shorter way to the answer