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Find the Values Of A And B Such that the Function Defined by F(X) = {(5, ", If X <= 2),(Ax +B, If 2 < X < 10),(21, If X >= 10 - CBSE (Commerce) Class 12 - Mathematics

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Question

Find the values of a and b such that the function defined by

`f(x) = {(5, "," if x <= 2),(ax +b, "," if 2 < x < 10),(21, "," if x >= 10):}` 

is a continuous function.

Solution

The given function is `f(x) = {(5, "," if x <= 2),(ax +b, "," if 2 < x < 10),(21, "," if x >= 10):}` 

It is evident that the given function f is defined at all points of the real line.

If f is a continuous function, then f is continuous at all real numbers.

In particular, f is continuous at = 2 and = 10

Since f is continuous at = 2, we obtain

On subtracting equation (1) from equation (2), we obtain

8a = 16

⇒ a = 2

By putting a = 2 in equation (1), we obtain

2 × 2 + b = 5

⇒ 4 + b = 5

⇒ b = 1

Therefore, the values of a and b for which f is a continuous function are 2 and 1 respectively.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 5: Continuity and Differentiability
Q: 30 | Page no. 161
Solution Find the Values Of A And B Such that the Function Defined by F(X) = {(5, ", If X <= 2),(Ax +B, If 2 < X < 10),(21, If X >= 10 Concept: Algebra of Continuous Functions.
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