Find the value of k so that the function f is continuous:

f(x)= {9x^2-4/3x-2, x≠-2/3 }

k , x=-2/3

Step-by-step explanation:

and

Remember that a function is continuous in x=a if

Since f is a rational function for every number different of , then f is continuous in these numbers.

Then we need that

As we are approaching -2/3 then we are taking values greater and less than -2/3. Therefore for the limit we use .

But observe that .

Then k must be .

let's verify that in effect f is continuous with .

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step-by-step explanation: