Question

Let f(x) = x³ - a³ x - a if x ≠ a, c if x = a. Find the value of c such that f is continuous at x = a?

Answer 1

The value of c that makes f continuous at x=a is -1.

Step-by-step explanation:

To find the value of c such that f is continuous at x = a, we need to equate the two expressions for f when x = a. Let's set up an equation using the given function:

f(x) = x³ - a³x - a if x ≠ a, c if x = a

Setting x = a, we get:

c = a³ - a³a - a

Now, we can simplify this equation and solve for c:

c = a³ - a⁴ - a

Since we know that a = 1, we can substitute this value in the equation:

c = 1 - 1⁴ - 1

c = 1 - 1 - 1

c = -1

Therefore, the value of c that makes f continuous at x = a is -1.