Question

f(x) = {
x2 − 4
_______
x − 2 if x < 2

ax2 − bx + 3 if 2 ≤ x < 3

4x − a + b if x ≥ 3
}
What are the values of a and b to make the function continuous?

Answer 1

way easier than it seems
\[\frac{x^2-4}{x-2}=x+2\] if \(x\neq 2\) so the limit at 2 is 4
set \(ax^2-bx+3\) should be 2 when \(x=2\) in other words
\[4a-2b+3=2\] or
\[4a-2b=-1\]

Answer 2

=O!

Answer 3

whoa typo sorry i meant
\[4a-2b=+3=4\] so
\[4a-2b=1\]

Answer 4

oh wait i got that part ^

Answer 5

just didnt know what to do with the bottom 2.

Answer 6

then replace \(x\) by 3 in the second two equations

Answer 7

12 - a + b = 9a - 3b + 3

Answer 8

you should get
\[12-a+b=9-3b+3\]

Answer 9

10a - 4b -9 = 0

Answer 10

ok right

Answer 11

or
\[9a-4b=9\]

Answer 12

damn i can't type
\[10a-4b=9\]

Answer 13

so.. do i just set that equal to the other 1..

Answer 14

\[4a-2b=1\]
\[10a-4b=9\] solve for \(a\) and \(b\)

Answer 15

k thx
i got it

Answer 16

yw