By applying the definition of continuity and knowing piecewise functions, we know that the solution to this system of linear equations is c = 10 and d = -8.
<h3>How to make a piecewise function continuous</h3>
According to the <em>functional</em> theory, functions are continuous for a given interval if and only if the function has an only value for each element of the interval. In the case of the <em>piecewise</em> function, we must observe these two conditions:
2 · x = c · x² + d, for x = 1 (1)
4 · x³ = c · x² + d, for x = 2 (2)
Then, we have the following system of linear equations:
c + d = 2 (1b)
4 · c + d = 32 (2b)
The solution to this system of linear equations is c = 10 and d = -8.
To learn more on piecewise functions: brainly.com/question/12561612
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