Question

Let f(x) =
\begin{cases}
-2 x+b, &\text{if}\ x< 5\\
\frac{-150}{x-b}, &\text{if}\ x\geq5
\end{cases}
There are exactly two values for b which make f(x) a continuous function at x=5. The one with the greater absolute value is

Answer 1

set left limit equal to right limit then solve for b

Answer 2

replace \(x\) by \(5\) in both expressions, set them equal, solve for \(b\)
you will get a quadratic equation in \(b\) hence the two solutions

Answer 3

which is another somewhat more prosaic was of exactly what @freckles said

Answer 4

i get -10+b=150/5-b and dont know what to do after

Answer 5

start with
\[(-10+b)(5-b)=150\] and solve that one

Answer 6

yes but then you get -bsquared+15b-300

Answer 7

is -50-150=-300?

Answer 8

ahh pellett thanks!!!

Answer 9

it still doesnt make sense

Answer 10

unless i distribute wrong

Answer 11

it really looks like your answer will be ugly unfortunately

Answer 12

oh you know what

Answer 13

i think there was a -150/(x-b)

Answer 14

was that considered earlier

Answer 15

not 150/(x-b)

Answer 16

ohh i put put postive instead of negative 150

Answer 17

i got it thank you very much

Answer 18

that should have a better pretty answer :)

Answer 19

its 20

Answer 20

gj you!