Hi guys, can anyone help me with this, Thanks a lot:)

Step-by-step explanation:

A function is continuous at a point if and only if:

So, we have the piecewise function:

And we want to find the value of k such that the function is continuous.

First, find the left hand limit of f(x):

Since we're coming from the left, we'll use the first equation. Thus:

Direct substitution:

Simplify:

Subtract and divide:

So, what this tells us is that for the function to be continuous, the right hand limit as  f(x) approaches 9 from the right must also be equal to 0.

Therefore:

Direct substitution:

Subtract 1 from both sides:

Divide both sides by -9:

Therefore, the value of k is 1/9.

So, our equation in the end is:

  k = 1/9

Step-by-step explanation:

In order for the function to be continuous at x=9, the values of the two expressions must be the same at x=9.

The first expression evaluates to ...

The second expression needs to have the same value:

a

step-by-step explanation:

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