The Total solution for NCERT class 6-12
Findthe values of a and b such that the functiondefined by
is a continuousfunction.
The given function f is
It isevident that the given function f is defined at all points ofthe real line.
If f isa continuous function, then f is continuous at all realnumbers.
Inparticular, f is continuous at x = 2and x = 10
Since f iscontinuous at x = 10, we obtain
On subtracting equation (1) from equation(2), we obtain
8a =16
⇒ a = 2
Byputting 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 isa continuous function are 2 and 1 respectively.