Class 11, Maths

Exercise 13.1

Question 28.

Let   f(x) = { a + bx, x < 1

                { 4        , x = 1

                {b - ax, x > 1

and if lim_x->1 f(x) = f(1), then what is the possible value of a and b?

Solution:

Given f(x) = { a + bx, x < 1

                { 4        , x = 1

                {b - ax, x > 1

Now, lim_x->1^- f(x) = lim_x->1 (a + bx) = a + b

and lim_x->1⁺ f(x) = lim_x->1 (b - ax) = b - a

Given, lim_x->1 f(x) = f(1)

=> lim_x->1^- f(x) = lim_x->1⁺ f(x) = f(1)

=> a + b = 4

and b - a = 4

After solving these two equations, we get

a = 0 and b = 4

So, the possible of a and b are 0 and 4