NDA 2020 Maths · Mathematics · Continuity and Differentiability · easy

The function f(x)=(x^2-5x+6)/(x-2) for x≠2 and f(2)=k is continuous at x=2. Then k equals

Single correct option

The function

f(x)=\dfrac{x^2-5x+6}{x-2}

for

x\ne2

and

f(2)=k

is continuous at

x=2

. Then

k

equals

Show answer and solution

Answer: (D) $-1$

Factor the numerator:

x^2-5x+6=(x-2)(x-3)

, so for

x\ne2

f(x)=x-3

and

\displaystyle\lim_{x\to2}f(x)=-1

. Continuity needs

f(2)=-1

, so

k=-1

. The value

0

is what the numerator gives on direct substitution, a

0/0

situation, and

1

is the result of a sign slip. The other root

3

is the zero of

f

for

x\ne2

and is not its limit at

2

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake