NDA 2025 Maths · Mathematics · Continuity and Differentiability · medium

The function f(x)=begincasesax+3,&x≤2\x^2-1,&x>2endcases is continuous at x=2 if a is equal to

Single correct option

The function

f(x)=\begin{cases}ax+3,&x\le2\\x^2-1,&x>2\end{cases}

is continuous at

x=2

a

is equal to

Show answer and solution

Answer: (B) $0$

The left value is

f(2)=2a+3

and the right limit is

2^2-1=3

. Continuity requires

2a+3=3

, so

a=0

. The options

1

-1

and

2

arise by equating

2a

to the wrong quantity, for example using

x^2-1

x=1

or comparing

a

with

3

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