Question

Find the constant a such that the function is continuous on the entire real line.

f(x) = { 7x², x≥1,
ax-9, x<1
a=__

Answer 1

The constant a that makes the function continuous on the entire real line is 16.

Step-by-step explanation:

To find the constant a such that the function f(x) is continuous on the entire real line, we need to ensure that the two parts of the function match at x = 1.

Therefore, we set the two expressions equal to each other and solve for a:

7x² = ax - 9

Substituting x = 1 into the equation:

7(1)² = a(1) - 9

7 = a - 9

a = 16

Thus, the constant a such that the function is continuous on the entire real line is a=16.