Question

If the function \( f(x) = ax + b \), \( 2 < x < 4 \), is continuous at \( x = 2 \) and 4, then the values of \( a \) and \( b \) are:

• A. \( a = 3, b = 5 \)
• B. \( a = 0, b = 3 \)
• C. \( a = 0, b = 5 \)
• D. \( a = 3, b = 0 \)

Hint:

To ensure continuity at certain points, solve for the coefficients using the given values at those points.

Answer 1

The Correct Option is B

Step 1: Apply continuity condition.
For continuity at \( x = 2 \) and \( x = 4 \), the function \( f(x) \) should not have any breaks at these points. By solving for \( a \) and \( b \), we find \( a = 0 \) and \( b = 3 \).
Thus, the correct answer is (2).