Question

Asked Sep 12, 2019

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Find the value of the constant cc that makes the following function continuous on (−∞,∞)(−∞,∞).

f(x)={cx+7 if x∈(−∞,7], cx^2−7 if x∈(7,∞)

I tried to format this as best I could, but it is supposed to be a piecewise function.

Step 1

We have been given a piecewise function and we need to determine the value of ‘c’ at which the given function is continuous on all real numbers.

Step 2

Since both the pieces of the given piecewise function are polynomials, therefore, we only need to check continuity at the point where the two pieces split, that is, x=7.

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