Question

If \( f(x) = \begin{cases} \frac{x^2 + 3x - 10}{x^2 + 2x - 15}, & x \neq -5 \\ a, & x = -5 \end{cases} \) is continuous at \( x = -5 \), then the value of \( a \) will be

• A. \( \frac{3}{2} \)
• B. \( \frac{7}{8} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{2}{3} \)

Hint:

To determine the value of \( a \) for continuity, solve the limit of the function as \( x \) approaches the point.

Answer 1

The Correct Option is B

Step 1: Check for continuity.
For the function to be continuous at \( x = -5 \), the limit as \( x \) approaches \( -5 \) must equal the function value at \( x = -5 \).
Step 2: Evaluate the limit.
By simplifying the expression for the limit, we find that \( a = \frac{7}{8} \). Final Answer: \[ \boxed{\frac{7}{8}} \]