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".)

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 .

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 by equating both side functions as:

Therefore, will make the function continuous for all x in .

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions