SOLUTION: Find the values of a and b that make f continuous everywhere.
f (x)=
{
x2−4x−2 if x<2
ax2−bx+3 if 2≤x<3
2x−a+b if x≥3 }
I dont unde
Algebra.Com
Question 453993: Find the values of a and b that make f continuous everywhere.
f (x)=
{
x2−4x−2 if x<2
ax2−bx+3 if 2≤x<3
2x−a+b if x≥3 }
I dont understand how i would solve this. Please help. Thank you. :)
Found 3 solutions by richard1234, stanbon, ValerieDavis:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
f is continuous if:
and
Here, we have the system of equations
Solving, we get a = 21/2 and b = 51/2.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the values of a and b that make f continuous everywhere.
f (x)=
{
1. x^2−4x−2 if x<2
2. ax2−bx+3 if 2≤x<3
3. 2x−a+b if x≥3 }
-----------------------------
Evaluate "1" at x = 2
f(2) = 2^2-4*2-2 = -6
--------------
Evaluate "3" at x = 3
g(3) = 2(3)-a+b = 6-a+b
----
So two of the points of "2" must be (2,-6) and (3,6-a+b)
____
Substitute those coordinates into "2"
to solve for "a" and for "b".
---
2. ax2−bx+3
----
(2,-6) gives you 4a-2b+3 = -6
2a - b = -9
---
(3,6-a+b) gives you a(9)-b(3)+3 = 6-a+b
10a - 4b = 3
--------------------
Solve the system:
2a - b = -9
10a -4b = 3
----------------------
Multiply thru 1st equation by 5:
10a - 5b = -45
10a - 4b = 3
---
Subtract to get:
b = 48
---
Solve for "a":
2a - b = -9
2a - 48 = -9
2a = 39
a = 39/2
---------------------
I'd suggest you check alll the arithmetic
here as mistakes can creep in.
======================================
Cheers,
Stan H.
Answer by ValerieDavis(6) (Show Source): You can put this solution on YOUR website!
Thanks guys for solve this question!
PS.
I still have nightmares about a math test coming up & I haven't done any of the problems in the book's chapters.
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