## anonymous one year ago Give the values of A and B for the function f(x)={Ax-B when x<=1, -24x when 1<x<5, Bx^2-A when x>= 5} to be continuous at both x = 1 and x = 5.

1. misty1212

HI!!

2. misty1212

this is not as hard as it may look replace $$x$$ by $$1$$ in both expressions $Ax-B$ and $-24x$

3. misty1212

if $$x=1$$the first one is $$A-B$$ and the second is $$-24$$ so you have on equation $A-B=-24$

4. misty1212

then put in $$x=5$$ in both $$-24x$$ and $$Bx^2-A$$

5. misty1212

this time you get $-120=25B-A$ as a second equation

6. misty1212

solve the system $A-B=-24\\25B-A=-120$ to find $$A$$ and $$B$$

7. anonymous

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

8. misty1212

i didn't do it, but i can check if you like

9. misty1212

yeah i get the same thing

10. anonymous

Don't worry about it, plugging it in will tell me if it's right or not.

11. anonymous

oh, thanks!

12. misty1212

$f(x) = \left\{\begin{array}{rcc} Ax-B & \text{if} & x <1 \\ -24x& \text{if} & 1\leq x\leq5\\ Bx^2-A&\text{if} &x>5 \end{array} \right.$

13. misty1212

just seeing if i could write it $\color\magenta\heartsuit$