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A day full of math games & activities. Find one near you.
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
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
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