Asked Feb 14, 2019

find the values of the constants a and/or b needed to make the following functions continuous for all real numbers x

piecewise f(x) = ax - 12/x - 3, if x not equal to 3, b, if x = 3


Expert Answer

Step 1

To fix the values of the unknown a and b to ensure the continuity of the given function

Step 2

In order that a function f(x) is continuous at a point x=p, two conditions have to be met: f should be defined at p and both left hand side and right hand side limits of f(x) at x=p must be equal to the value f(p).

Step 3

In our case, we are looking for the continuity of f(x) at...

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