Question

Find all values of x for which the function y=(2(8-5x))/(x+1)

Answer 1

i think question is incomplete !

Answer 2

is differentiable.

Answer 3

y=([\sqrt{8-5x}\])/(x+1)...it's a square root also..not a two

Answer 4

\[f(x)=\frac{\sqrt{8-5x}}{x+1}\]

Answer 5

yes, that's what it looks like!

Answer 6

ok u must check for continuity first

Answer 7

when I graphed it, it looked like 1/x graph

Answer 8

yeah its something like that..maybe

Answer 9

so how do I check for continuity?

Answer 10

ok u have some restrictions here..

division by zero is not allowed
under radical cant be negative

Answer 11

actually u must find domain of ur function

Answer 12

domain is x=-1

Answer 13

\[x\neq -1\]

Answer 14

ohyeah you're right

Answer 15

and what about radical?

Answer 16

what's radical?

Answer 17

square root

Answer 18

x\[\neq5/8\]

Answer 19

er 8/5

Answer 20

when u have something like \[\sqrt{x}\] u must have \[x\ge0\] right ?

Answer 21

yes

Answer 22

so what about the expression under square root sign?

Answer 23

\[x \neq 8/5\]

Answer 24

emm i mean u must have \(8-5x\ge0\) and this leads to\[x\le\frac{8}{5}\]make sense?

Answer 25

oh yes sorry i meant to do that sign instead of the nonequal sign

Answer 26

it does make sense

Answer 27

good

Answer 28

ok so the domain of function becomes\[x\le \frac{8}{5} \ \ \text{and} \ \ x\neq-1\]

Answer 29

or u can write it like this\[(-\infty,-1)\cup (-1,\frac{8}{5}]\]

Answer 30

got it. so is that where it's differentiable?

Answer 31

yes thats it ... and just one more point

function is not continous at end points \(x=-1\) and \(x=\frac{8}{5}\) so it'll not be differentiable at that points...

Answer 32

ok thank you so much! i appreciate it :)

Answer 33

very welcome :)