Question

Let f(x)={4x−1, if x≤3......
.............−5x+b, if x>3
If f(x) is a function which is continuous everywhere, then we must have
b=

Answer 1

do the left limit and right limit for x=3
and set them equal and solve for b

Answer 2

ohh i see

Answer 3

how would i go about solving this one...same way?
For what value of the constant c is the function f continuous on (−∞,∞) where f(x)=...... cx+8 if x∈(−∞,2] .......
cx^2−8 if x∈(2,∞)......

Answer 4

yes you look at the left limit and right limit for x=2

Answer 5

and set them equal

Answer 6

hey so for the first problem...i used 4(3)-1 = 11 and -5(3.1)+b = -15.5 + b. So I set -15.5 + b = 11 and I did the algebra and ended up with -4.5. what did i do wrong?

Answer 7

\[4(3)-1=-5(3)+b\]

Answer 8

yeah shouldnt u get a -4.5 after you do the algebra

Answer 9

i don't know
i can perform the operations if you want me too

Answer 10

4(3)=12
12-1=11
-5(3)=-15
so we have
11=-15+b
By adding 15 on both sides we get
26=b

Answer 11

oh snap i did it backward haha thanks

Answer 12

can i use 1.5 and 3 for the second question

Answer 13

i don't understand

Answer 14

how would i go about solving this one...same way? For what value of the constant c is the function f continuous on (−∞,∞) where f(x)=...... cx+8 if x∈(−∞,2] .......
cx^2−8 if x∈(2,∞)......

once again i have to approach from both sides...if im approaching from left can I use x=1.5 and right x=3?

Answer 15

what no just before we plugged in 3 for both sides
here we do 2

Answer 16

\[c(2)+8=c(2)^2-8\]

Answer 17

now solve for c