determine the value of k so that the piecewise function below is continuous.f(x)={kx−1 k+5x. if x≤3 if x>3
To determine the value of k for the piecewise function to be continuous, we need to ensure that the two parts of the function are equal when x = 3
To determine the value of k for the piecewise function to be continuous, we need to ensure that the two parts of the function are equal when x = 3.
When x ≤ 3, the function is defined as kx – 1.
When x > 3, the function is defined as k + 5x.
So we need to find the value of k that makes these two expressions equal at x = 3.
Setting these two expressions equal to each other, we have:
kx – 1 = k + 5x
Now we can substitute x = 3:
k(3) – 1 = k + 5(3)
3k – 1 = k + 15
Rearranging the equation:
3k – k = 15 + 1
2k = 16
Dividing by 2:
k = 8
Therefore, to make the piecewise function continuous, the value of k should be 8.
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