Suppose f (x) = {a + bx, x < 1, 4, x = 1 and b - ax, x > 1} and if lim ₓ→₁ f(x) = f (1) what are possible values of a and b?

Solution:

The given function is f (x) = {a + bx, x < 1, 4, x = 1 and b - ax, x > 1}

We will calculate the left-hand and right-hand limits.

lim ₓ→₁₋ f (x) = limₓ→₁ (a + bx) = a + b

lim ₓ→₁₊ f (x) = limₓ→₁ (b - ax) = b - a

We have f (1) = 4

It is given that lim

limₓ→₁ f (x) = f (1)

Therefore,lim ₓ→₁₋ f (x) = lim ₓ→₁₊ f (x) = limₓ→₁ f (x) = f (1)

Hence, a + b = 4 and b - a = 4

On solving these two equations, we obtain

a = 0 and b = 4

Thus, the respective possible values of a and b are 0 and 4

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NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 28

Suppose f (x) = {a + bx, x < 1, 4, x = 1 and b - ax, x > 1} and if lim ₓ→₁ f(x) = f (1) what are possible values of a and b?

Summary:

Suppose f (x) = {a + bx, x < 1, 4, x = 1 and b - ax, x > 1} and if lim ₓ→₁ f(x) = f (1), then the respective possible values of a and b are 0 and 4