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Suppose f(x)={5x7x+c for x≥9, for x<9. In order to make f(x) continuous for all x in (−[infinity],[infinity]), what number should c be equal to? c= 9 (If there is no possible value of c that makes f(x) continuous for all real x, enter "none".)

User Hugo Noro
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1 Answer

4 votes

Answer:


c=-18

Explanation:

We have been given a piece-wise function. We are asked to find the value of possible value of c that will make the function continuous for all x in
(-\infty,\infty).


\left \{ {{f(x)=5x,\text{ for }x\geq 9} \atop {f(x)=7x+c,\text{ for }x>9}} \right.

We know that a piece-wise function is continuous when right hand side limit is equal to left hand side limit.

To find the value of c that will make function continuous, we need to find the value of c at
x=9 by equating both side functions as:


7x+c=5x


7(9)+c=5(9)


63+c=45


63-63+c=45-63


c=-18

Therefore,
c=-18 will make the function continuous for all x in
(-\infty,\infty).

User Bkcollection
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