CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Find the values of $$a$$ and $$b$$ such that the function defined by $$f(x) = \left\{\begin{matrix} 5,& if & x\leq 2\\ ax + b, & if & 2 < x < 10\\ 21, & if & x \geq 10\end{matrix}\right.$$ is a continuous function.


Solution

$$f(x) = \left\{\begin{matrix} 5,& if & x\leq 2\\ ax + b, & if & 2 < x < 10\\ 21, & if & x \geq 10\end{matrix}\right.$$

If the function $$f(x) $$ is a continuous function, then
$$f(2) = f(2^+)$$ and $$f(10^{-}) = f(10)$$

$$I: f(2) = f(2^+)$$
$$5 = 2a+b$$ ... (i)

$$II: f(10^{-}) = f(10)$$
$$10a+b = 21$$ ...(ii)

from (i) and (ii), we get
$$a = 2, b = 1$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image