Find all values of c such that the domain of the following function is the set of all real numbers f(x) = (x + 7) / (x^2 + 2cx + 14)

Step-by-step explanation:

For the function to have a domain of all reals, the denominator cannot have a value of zero. x^2 + 2cx + 14 will not have zero as a root if it has no real solutions. A quadratic equation has no solutions when the discriminant is negative.

b^2 - 4ac < 0

(2c)^2 - 4(1)(14) < 0

4c^2 - 56 < 0

4c^2 < 56

c^2 < 14

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.