Q12 of 45 Page 1

Find the value of a and b such that the following function f(x) is a continuous function:

f (x) = 5 x less than equal to 2 ax+b 2<x<10 21 x geater than or equal to 10


Now,


F(x) is continuous at x=2


If L.H.L=R.H.L=f(2)


Then,



L.H.L



5


R.H.L




2a + b


Since, L.H.L=R.H.L


2a + b=5 …(i)


Now,


F(x) is continuos at x=10


If L.H.L=R.H.L=f(10)



L.H.L




10a + b


R.H.L



21


Since, L.H.L=R.H.L


10a + b=21 …(ii)


Now, From (i) and (ii)


10a + (5 - 2a)=21


8a=16



a=2


Putting the value of a in equation (i)


2(2) + b=5


4 + b=5


B=5 - 4


b=1


Hence, The value of a = 2 and b=1


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