For what values of a and b is the following function continuous at every x? f(x)={0x≤−1ax−b−1&lt;x&lt;310x≥3

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For what values of a and b is the following function continuous at every x?  f(x)={0x≤−1ax−b−1&amp;lt;x&amp;lt;310x≥3

Heather Fulton · Accepted Answer

Step 1 Here according to rhe question, f is constinuous So, if limx⇒−1−1f(x)=limx⇒−1+f(x) limx⇒−10=limx⇒−1ax−b а0=−а−b аа+b=0 ∴a=−b Step 2 So, similarly f is constinuous if limx⇒3−f(x)=limx⇒3+f(x) limx⇒3(ax−b)=limx⇒310 3a−b=10 Step 3 We know, a=−b So, −3b−b=10 −4b=10 b=−104 b=−52 We know, a=−b ∴a=52

Mary Nicholson · Accepted Answer

Step 1    limx→−3−f(x)=limx→−3−−0=0    limx→−3+f(x)=limx→−3+ax−b=−a−b    limx→3−f(x)=limx→3−ax−b=a−b    limx→3+f(x)=limx→3+10=10    For the function to be continuous, we need the limits at x=3 and x=−3 to exist (and then these would also be the values of the function at that point).    Step 2    a=5/2, b=-1/2  a=5/2,b=−1/2  Solve for a,b the linear equations:    a=−b    −b−3b=10    −4=10    −104    −52    ⇒a=52

For what values of a and b is the following

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