clara1223
  • clara1223
Give the values of A and B for the function f(x)={Ax-B when x<=1, -24x when 1= 5} to be continuous at both x = 1 and x = 5.
Mathematics
katieb
  • katieb
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
this is not as hard as it may look replace \(x\) by \(1\) in both expressions \[Ax-B\] and \[-24x\]
misty1212
  • misty1212
if \(x=1\)the first one is \(A-B\) and the second is \(-24\) so you have on equation \[A-B=-24\]

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misty1212
  • misty1212
then put in \(x=5\) in both \(-24x\) and \(Bx^2-A\)
misty1212
  • misty1212
this time you get \[-120=25B-A\] as a second equation
misty1212
  • misty1212
solve the system \[A-B=-24\\25B-A=-120\] to find \(A\) and \(B\)
clara1223
  • clara1223
Thanks so much! I got that A= -30 and B=-6. I'm just going to plug them back in to make sure they work! ti\njhj
misty1212
  • misty1212
i didn't do it, but i can check if you like
misty1212
  • misty1212
yeah i get the same thing
clara1223
  • clara1223
Don't worry about it, plugging it in will tell me if it's right or not.
clara1223
  • clara1223
oh, thanks!
misty1212
  • misty1212
\[f(x) = \left\{\begin{array}{rcc} Ax-B & \text{if} & x <1 \\ -24x& \text{if} & 1\leq x\leq5\\ Bx^2-A&\text{if} &x>5 \end{array} \right. \]
misty1212
  • misty1212
just seeing if i could write it \[\color\magenta\heartsuit\]

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