Question

For the function f(x) = (x²-7x-10)/(bx-2), for x ≠ 2, for what value of b is f continuous at x=2?

a) b = 2
b) b = 1
c) b = 5
d) b = -2

Answer 1

To determine the value of b for which the function f(x) = (x²-7x-10)/(bx-2) is continuous at x=2, we need to check if the limit of the function as x approaches 2 exists and is finite.

Step-by-step explanation:

To determine the value of b for which the function f(x) = (x²-7x-10)/(bx-2) is continuous at x=2, we need to check if the limit of the function as x approaches 2 exists and is finite. If the limit exists, we set it equal to the value of the function at x=2 and solve for b.

First, let's evaluate the limit:

limx→2 f(x) = limx→2 (x²-7x-10)/(bx-2)

We can simplify the function by factorizing the numerator and canceling the common factors:

limx→2 f(x) = limx→2 (x+2)(x-5)/(bx-2)

To find the value of b for which the limit is finite, we need to ensure that the denominator does not become zero. This means that b cannot be equal to 2. Therefore, the correct answer is (b) b = 2.