Question

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".)

Answer 1

Answer:

$c=-18$  

Step-by-step 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 $(-\infty,\infty)$.