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42)(-4,X-4ax + b, -4s x< -3f(x)=5,x > -3

Question

Find numbers a and b so that f is continuous at every point.

42)
(-4,
X-4
ax + b, -4s x< -3
f(x)=
5,
x > -3
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42) (-4, X-4 ax + b, -4s x< -3 f(x)= 5, x > -3

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check_circleAnswer
Step 1

Given,

 

(-4
x<-4
f (x)={ax + b, -4sxs-3
5,
x > -3
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(-4 x<-4 f (x)={ax + b, -4sxs-3 5, x > -3

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Step 2

We check the continuity of the given function at the points x = -4 and x = -3.

Step 3

At x = -4:

&nb...

f(-4) a-4)b=-4a+b
LHL lim f(x) = lim (-4) =-4
x+-4
X-4
RHL limf(x)lim (ax +b)
a-4) +b = -4a+b
*-4
x+-4
Since f must be continuous at every point, therefore
-4ab4 >(1)
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f(-4) a-4)b=-4a+b LHL lim f(x) = lim (-4) =-4 x+-4 X-4 RHL limf(x)lim (ax +b) a-4) +b = -4a+b *-4 x+-4 Since f must be continuous at every point, therefore -4ab4 >(1)

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