Question

For what value of the constant c is the fu f(a)={(ca+3 if a<=4),(c(a)²-3 if a>4):}

Answer 1

To determine the value of constant c for the function to be continuous at a=4, you need to equate the two expressions of the function at that point and solve for c. After substituting a=4 into both expressions and solving the resulting equation, you would find that c must be 0.5.

Step-by-step explanation:

The student's question is asking for the value of the constant c in a piecewise function that has different definitions depending on the value of a. In order to find the value of c that makes this function continuous at a=4, we need to ensure that both pieces of the function have the same value at a=4. This means solving the equation ca+3=c(a)²-3 when a=4.

Let's plug a=4 into the equation and solve for c:

1. 4c + 3 = c(4)² - 3
2. 4c + 3 = 16c - 3
3. 3 + 3 = 16c - 4c
4. 6 = 12c
5. c = 6 / 12
6. c = 0.5

The constant c must be 0.5 for the function to be continuous at a=4.